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FORMULAS 



IN 



GEARIN G 



FOURTH EDITION. 



WITH PRACTICAL SUGGESTIONS. 



PROVIDENCE, R. I., U. S. A 

PUOWNf 6c SHARPS MAN L' KACTUiUN'J <w^ . 

1905. 














I: 







FORMULAS 



IN 



GEARING 



FOURTH EDITION. 



WITH PRACTICAL SUGGESTIONS- 



providence, R. I., U. S. A. 

BROWN & SHARPE MANUFACTURING COMPANY. 
1905. 



V\V :>/,( ") 




Copyright 

1900, 1905, 

By BROWN 6 SHARPE MFG. 00. 



PREFACE. 

It is the aim, in the following pages, to condense as much 
as possible the solution of all problems in gearing which in the 
ordinary practice may be met with, to the exclusion of prob- 
lems dealing with transmission of power and strength of 
gearing. The simplest and briefest being the symbolical 
expression, it has, whenever available, been resorted to. The 
mathematics employed are of a simple kind, and will present 
no difficulty to anyone familiar with ordinary Algebra and 
the elements of Trigonometry. 



CONTENTS. 

FORMULAS IN GEARING. 



CHAPTER I. 

Page 
Systems of Gearing 9 

CHAPTER II. 
Spur Gearing — Formulas — Chordal Thickness of Gear Teeth 12 

CHAPTER III. 

Bevel Gears, Axes at Right Angles — Formulas — Bevel Gears, Axes at 
any Angle — Formulas — Diameter Increment — Undercut in Bevel 
Gears 16 

CHAPTER IV. 
Worm and Worm Wheel, Formulas — Undercut in Worm Wheels 25 

CHAPTER V. 

Spiral or Screw Gearing — Axes Parallel — Axes at Right Angles — 
Axes at any Angle — General Formulas 29 

CHAPTER VI. 
Internal Gearing — Internal Spur Gearing — Internal Bevel Gears 38 

CHAPTER VII. 
Dimensions and Form for Bevel Gear Cutters 44 

CHAPTER VIII. 

The Indexing of any Whole or Fractional Number — Differential 
Indexing 49 

CHAPTER IX. 

The Gearing of Lathes for Screw Cutting — Simple Gearing — Com- 
pound Gearing — Cutting a Multiple Screw 58 



TABLES. 

Page 

Corrected T and Corrected S for Gear Teeth 74, 75 

Tooth Parts— Circular Pitch— Diametral Pitch 68-71 

Diameter Increments 78-81 

Angles of Edge and Angles of Face 84-92 

Cutters for Use in Cutting Bevel Gears 94, 95 

Natural Sines and Cosines — Natural Tangents and Cotangents. . . .98-115 

Angles for Gashing Worm Wheels 1 18, 1 19 

Prime Numbers and Factors 12 1-155 

Decimal Equivalents of Parts of an Inch — Decimal Equivalents of 
Millimetres and Fractions of Millimetres 158, 159 



FORMULAS IN GEARING. 



CHAPTER I. 

SYSTEMS OF GEARING. 

(Figs, x, a.) 

There are in common use two systems of gearing, viz.: the 
involute and the epicycloidal. 

In the involute system the outlines of the working parts of a 
tooth are single curves, which may be traced by a point in a 
flexible, inextensible cord being unwound from a circular disk 
the circumference of which is called the base circle, the disk 
being concentric with the pitch circle of the gear. 



3<***J 



^^""h^: 


^^^"^-^^1 










? — 


-~-^^ i * , *n»r*^*^^/r4 ^i* ^- - ^s. 








s4 ^*^5 




< 


>' 






Fig. 


1. 





In Fig. i the two base circles are represented as tangent to 
the line P P. This line (P P) is variously called " the line of 
pressure," a the line of contact," or " the line of action." 



IO 



BROWN & SHARPE MFG. CO. 



In our practice this is drawn so as to make with a normal 
to the center line (O O') 14%°, or with the center line 75^°. 

The rack of this system has teeth with straight sides, the two 
sides of a tooth making, together, an angle of 29 (twice 

i4#°>. 

This applies to gears having 30 teeth or more. For gears 
having less than 3b teeth special rules are followed, which are 
explained in our " Practical Treatise on Gearing." 




Fig. 2. 



In cpicycloidaly or double-curve teeth, the formation of the 
curve changes at the pitch circle. The outline of the faces of 
epicycloidal teeth may be traced by a point in a circle rolling 
on the outside of pitch circle of a gear, and the flanks by a point 
in a circle rolling on the inside of the pitch circle. The faces 
of one gear must be traced by the same circle that traces the 
flanks of the engaging gear. 

In our practice the diameter of the rolling or describing 
circle is equal to the radius of a 15-tooth gear of the pitch 
required ; this is the base of the system. The same describing 
circle being used for all gears of the same pitch. 



BROWN & SHARPE MFG. CO. II 

The teeth of the rack of this system have double curves, 
which may be traced by the base circle rolling alternately on 
each side of the pitch line. 

An advantage of the involute over the epicycloidal tooth is, 
that in action gears having involute teeth may be separated a 
little from their normal positions without interfering with the 
angular velocity, which is not possible in any other kind of 
tooth. 

The obliquity of action is sometimes urged as an objection 
to involute teeth, but a full consideration of the subject will 
show that the importance of this has been greatly over-esti- 
mated. 

The tooth dimensions for both the involute and epicycloidal 
gears may be calculated from the formulas in Chapter IX. 



CHAPTER II. 

SPUR GEARING. 

(Figs. 3, 4.) 

Two spur gears in action are comparable to two correspond- 
ing plain rollers whose surfaces are in contact, these surfaces 
representing the pitch circles of the gears. 

Pitch of Gears. 

For convenience of expression the pitch of gears may be 
stated as follows : 

Circular pitch is the distance from the center of one tooth to 
the center of the next tooth, measured on the pitch line. 

Diametral pitch is the number of teeth in a gear per inch of 
pitch diameter. That is, a gear that has, say, six teeth for each 
inch in pitch diameter is six diametral pitch, or, as the expres- 
sion is universally abbreviated, it is " six pitch." This is by 
far the most convenient way of expressing the relation of 
diameter to number of teeth. 

Module is the pitch diameter of a gear divided by the 
number of teeth. 

Chordal pitch is the distance from center to center of two 
adjacent teeth at the pitch line measured on the chord. 




Fig. 3. 



BROWN * SHARPE MFG. CO. 



13 




CHORDAL 

THICKNESS 

OF 

GEAR TEETH. 

The dimensions of 
Tooth Parts as given 
in the tables, pages 68 
to 71, are correct ac- 
cording to the defi- 
nition of Tooth Parts ; 
but, as the pitch line 
of gears is curved, the 
thickness of a tooth 
will not be measured 
on the pitch line if 
the Caliper is set to 
the figures given in 
Tables of Tooth Parts. 
To measure the tooth 
accurately the Caliper 
must be set to the 
Chordal Thickness. 



GEAR TOOTH 1 P. 

CHORDAL THICKNESS OF 

TEETH FOR GEARS ON A 

BASIS OF 1 DIAMETRAL 

PITCH. 



S = Distance from pitch line to top of teeth. 

S Corrected ==H+S. 

N = Number of teeth in gear. 



H = R(i— cos./?') 



T= Chordal thickness of Tooth. T = D' sin. /?' 

H = Height of Arc. 

D' = Pitch Diameter. 

R = Pitch Radius. 

/J' = 90° divided by the number of teeth. 

Not*— When the tooth of a gear is measured, add the height of arc to (S). 

For tables giving corrected T and corrected S see pages 
74 and 75. 



J 4 » BROWN & SHARPE MFG. CO. 

FORMULAS. 

N = number of teeth. 
s = addendum and module. 
/ = thickness of tooth on pitch line. 
/= clearance at bottom of tooth. 
D" = working depth of tooth. 
D" + / = whole depth of tooth. 
d = pitch diameter. 
<? = outside diameter. 
P' = circular pitch. 
P = diametral pitch. 
C = center distance. 

6 = half the angle subtended by the circular pitch. 
p _ N + 2 

d' 

f-5.' • 

P' = ? 

p 



_ d- _ <r 



N. N + 2 
/=J.P' = _5_ 

2 2 P 



IO 

-+/=^(i+^) =-3.683 P' 



D"=2/ory 



D* +/= LIS1 = .6866 F 
P° = d sin 



F 

180° 

N 



f. i8o° . , P° 
tf = - !r ;s 1 n<y = - 

i8o° 

d' =. d + 2 s 

. NP' 
a = 



BROWN ft SHARPE MFG. CO. 



l 5 



Comparative Sizes of Gear Teeth. 
Involute. 




8 p 



9 p 



Fig. 4. 



CHAFTTBR III. 

BEVEL GEARS.— AXES AT RIGHT ANGLES. 

(Fi*. 5-) 




BROWN & SHARPE MFG. CO. 1 7 



FORMULAS. 



~ a - J Number of teeth i S? a - n 



N b = J ( pinion 

P = diametral pitch. 

P' = circular pitch. 

= ) center angle = angle of edge j gear, 
or pitch angle ( pinion. 

ft = angle of top. 

ft = angle of bottom. 



" 6 = ) 



- I angle of face \ *f*?' 
= ) ° ( pinion. 



t= [cutting angle {^^ 

A = apex distance from pitch circle. 

A' = apex distance from large bottom of tooth. 

d = pitch diameter. 
d' = outside diameter. 

s = addendum and module. 

/ = thickness of tooth at pitch line. 
/ = clearance at bottom of tooth. 
D" « working depth of tooth. 
D" +/= whole depth of tooth. 
2 a = diameter increment. 

b = distance from top of tooth to plane of pitch circle. 
F = width of face. 



i8 



BROWN & SHARPE MFG. CO. 



tan<r a = *•_ ; tana F A J 
N 6 N a 

. x? 2 sin a >, j 

tan p = — _ — ; or tan = _ • 
N A 

tan ft = sina ( 2 + £) = 2 3 I 4 sin a ^ = i± / 

N N ' H A ' 

^a = 9o° - (a. + /8) \g b = 9 o° - <a» + /?) 
A = a— ft' (See Note, page 46.) 



A = 

N 



A = 

2 P sin a 

A'=_A_ A'= 5 _ 

cos /8' 2 P sin « cos p 

A = . **' ^ cos /3 
sin (a + /?) 

2 A sin a 

v N N P' ,, ,_,_ 

a= — or = a = a + 2 a 

P ;r 

2 a = 2 j cos a (See pages 78 to Si.) 

, . {a for gear = b for pinion 

o=- a tan flf ■< r • • r r 

( <? for pinion = b for gear 

P = n P'= - 

p r p 

j = 2 = ^1 = .3183 P' x = Atan/? 

P 7T 

*+/== .3685 P' j +/=Atan/?' 

' + /=7(' + fo) D "=" 

F = i + ^ or = 2 P' to 3 P' 
P 7 

Note. — Formulas containing notations without the designating letters a and b 
apply equally to either gear or pinion. If wanted for one or the other, the respective 
letters are simply attached. 



BROWN k SHARPE MFG. CO. 



*9 



BEVEL GEARS WITH AXES AT ANY ANGLE 



Pinion 




Fig. 6. 



20 BROWN & SHARPE MFG. CO. 



FORMULAS. 

C = angle formed by axes of gears. 

]J» Z \ number of teeth \ $r*?' 
IM 6 = J ( pinion. 

P = diametral pitch. 

P' = circular pitch. 

al = } an S le of ed S e = P itch an S le { pmYon. 
/3 = angle of top. 
ff = angle of bottom. 

£= [angle of face j^. 

\ : Z\ cutting angle] g"^ 

A = apex distance from pitch circle. 
A' = apex distance from large bottom of tooth.' 

d = pitch diameter. 
d' = outside diameter. 
2 a = diameter increment. 

b = distance from top of tooth to plane of pitch circle. 

Note.— The formulas for tooth parts as given on page 14 apply equally to these cases. 



BROWN & SHARPB MFG. CO. 21 



sin C * N * . * ^ 

tan ar„ = — ; or cot a a = -- — : — — + cot C 



N„ 


+ cosC 

sin C 
+ cos c' 


or cot 


«6 


— 


N a 


sin 

N a 


C 


Na 


N 6 


sin 


C 



tan a b = — — ; or cot a b = -- — : — — + cot C 

Ng 

Nft 

Note. — The above formulas are correct only for values of C less than 90 . 
If C is greater than 90 , consult page 23. 



A 2 sin a s 

tan p = — — — : or tan p = -r- ; 
N A 

tan /T = !*^±£) = M^ . tan ff = £±/ . 



^ a = 90° — (ar a + /?) for Cases I and II. 

g a = fi, for Case III. 

ga = 9 o° — (a a — /J) for Case IV. 

^6 = 90°— O& + ft) 

(See page 46.) 



h = 


a 


-P 




A = 




N 




2 


Psin 


a 


A' = 


A 

" cos/?' 




d = 


N 
P 


or = 


N P' 



(for Cases I and II, 

1 and pinions in Cases III and IV. 

d' = d, for gear in Case III. 

d' = d — 2 a , for gear in Case IV. 

2 a = 2 s cos ot 

b = j sin tf 

Note. — Formulas containing notations without the designating letters a and & 
apply equally to either gear or pinion. If wanted for one or the other, the 
respective letters are simply attached. 



22 



BROWN & SHARPE MFG. CO. 




BROWN A SHARPE MFG. CO. 2 3 



The formulas given for a a and a b (when C, N and N b are 
known) undergo some modifications for values of C greater 
than 90 . 

For bevel gears at any angle but 90 we may distinguish 
four cases ; C, N a , N 6 being given. 

/. Case. See pages 19 and 21^ 

77. Case. C is greater than 90 . 

sin (180 — C) A sin (180 — C 
tan ar a = * L- ; tan a b = — * 

il- & -cos (180-C) ^-°-cos (180-C) 

III. Case. a a = 90 ; a b = C — 90 

IV. Case. 

«™ ~ sin E . _ _ sin E 

tan a a = — ; tan a b = 



cos E - ^ ^- a - cos E 

For an example to apply to Case III., the following condi- 
tion must be fulfilled : 

N a sin (C - 90 ) = N b 

To distinguish whether a given example belongs to Case II. 
or case IV., we are guided by the following condition : 

U • N *in (C - nn°\ i smaller than N * we have Case H - 

is . IN sin (U 90 ) \ iarger than Nfc> we have case IV . 

Diameter Increment. 

The ratio being given or determined, to find the outside 
diameter, divide the figures given in table, pages 78 to 81, 
for gear and pinion by pitch (P) and add the quotient to the 
pitch diameter. 

EXAMPLE. — Required, the outside diameters of a pair of 
bevel gears, 10 P, 35 T into 23 T. Referring to the table, 
the diameter increments are found to be for the gear 1.10 
and for the pinion 1.67. 

1. 10 -r- 10 = .110; 3.5 pitch diameter + .110 = 3.610 outside 
diameter of gear. 

1.67 -7- 10 = .167; 2.3 pitch diameter + .167 = 2.467 outside 
diameter of pinion. 



24 BROWN & SHARPE MFG. CO. 



UNDERCUT IN BEVEL GEARS. 

By undercut in gears is understood a special formation of 
the tooth, which may be explained by saying that the elements 
of the tooth below the pitch line are nearer the center line of 
the tooth than those on the pitch line. Such a tooth outline is 
to be found only in gears with few teeth. In a pair of bevel 
gears where the pinion is low-numbered and the ratio high, we 
are apt to have undercut. For a pair of running gears this 
condition presents no objection. Should, however, these gears 
be intended as patterns to cast from, they would be found use- 
less, from the fact that they would not draw out of the sand. 
We have stated on page io(see Fig. i) that the base of our 
involute system is the 14^° pressure angle. If a pair of bevel 
gears with teeth constructed on this basis have undercut, we 
can nearly eliminate the undercut — and for the practical work- 
ing this is quite sufficient— by taking as a basis for the con- 
struction of the tooth outline a pressure angle of 20 . 

The question now is : When do we and when do we not 
have undercut ? Let there be : 

N = number of teeth in gear. 
n = number of teeth in pinion-. 

n V N a + n % __ p 
N 
where we have undercut for/ less than 30. 

This formula is strictly correct for epicycloidal gears only. 
It is, however, used as a safe and efficient approximation for 
the involute system. 



CHAPTER IV. 



WORM AND WORM WHEEL. 

(Fig. 8.) 




26 BROWN & SHARPE MFG. CO. 

FORMULAS. 

L = lead of worm. 

N = number of teeth in gear. 

tn = turns per inch of worm. 

*/= diameter of worm. 
d' = diameter of hob. 
T = throat diameter. 
B = blank diameter (to sharp corners). 
C = distance between centers. 

o = thickness of hob-slotting cutter. 

/= width of lands at bottom. 

b = pitch circumference of worm. 

v = width of worm thread tool at end. 
«;= width of worm thread at top and width of hob 
tool at end. 

P = diametral pitch. 

P l = circular pitch for worm wheels or axial pitch for 
worms. 

D = pitch diameter of worm wheel. 

See figure 8. 

s = addendum and module. 
t = thickness of tooth at pitch line. 
t n = normal thickness of tooth. 
/= clearance at bottom of tooth. 
D" = working depth of tooth. 
D" 4- / = whole depth of tooth. 

6 = angle of tooth of worm wheel with its axis, or the 
angle of thread of worm with a line at right angles to its axis. 
If the lead is for single, double, triple, etc., thread, then 

L = P', 2 P', 3 P', etc. 
In multiple threaded worms and their mating wheels, if 
the angle # is more than 15° the tooth parts should be 
figured on the normal as for spiral gears. In using the 
formulas for spiral gears, it should be borne in mind that 
while P' is the axial pitch for worms it is the circular pitch 
for spiral gears. 



■:•} 



BROWN A SHARPE MFG. CO. 27 



a = 


6o° to 90 


L = 


. 1 

m 




P' = 


N + 2 




D = 


= N_P'_ 
n 


N 
P 


T = 


■? + « 


\ 


b = 


7T (^ — 2 S) 


tan 


6 = h 

b 


j Pra< 


/" = 


■ /cos d 




r' = 


d 

- — 2 s 

2 




r* = 


= r x + D" + / 


C = 


D + d 


■ s 



Practical only when width of wheel on wheel pitch circle 
is not more than % pitch diameter of worm. 



tj _ r« , / 1 1 _, _ _ Ot\ A measurement of sketch is generally 

B - T + 2 \r - r cos -j suffic i en t. 

d' = d+ if 
*=. 3 iP' 

W-.335P' 



Note.— The notations and formulas referring to tooth parts, given on page 14 for 
spur gears, apply to worm wheels, and are here used. 

Note. — Hob and worm should be marked, as per example : 
4 turns per 1'' single .25 P'; .25 L. 
2 turns per 1" double .25 P'; .50 L. 



28 



BROWN & SHARPE MFG. CO. 



UNDERCUT IN WORM WHEELS. 

In worm wheels of less than 30 teeth the thread of the worm 
(being 29 ) interferes with the flank of the gear tooth. Such 
a wheel finished with a hob will have its teeth undercut. To 
avoid this interference two methods may be employed. 

First Method. — Make throat diameter of wheel 



■ cos* 14^°^ +4* 



or 



T = :237_N + 4, 

This formula increases the throat diameter, and conse- 
quently the center distance. The amount of the increase can 
be found by comparing this value of T with the one as obtained 
by formula on page 27. To keep the original center distance, 
the outside diameter of the worm must be reduced by the 
same amount the throat diameter is increased. 

Second Method. — Without changing any of the dimensions 
we found by the formulas given on page 2 7, we can avoid the 
interference to be found in worm wheels of less than 30 teeth 
by simply increasing the angle of worm thread. We find the 
value of this angle by the following formula ; 
Let there be 

2 y = angle of worm thread. 

N = number of teeth in worm wheel. 



cos v = 4/ 1 — — 

y N 

From this formula we obtain the following values : 



N 


29 

30X 


28 


27 


26 


25 


24 


23 


22 


21 


20 


2 Y 


31 


3i# 


32K 


3*tt 


33#34# 


35 


36 


37 


N 


19 


18 


17 


16 


15 


14 


13 


12 




2 y 


3* 


39 


40 


4i# 


42^ 


W/2 


46% 


48 



As this latter formula involves the making of new hobs in 
many cases, on account of change of angle, we prefer to reduce 
the diameter of worm as indicated by first method, if the dis- 
tance of centers must be absolute. 



CHARTER V. 



SPIRAL OR SCREW GEARING. 

(Figs. 9, xo, ii.) 




Fig. 9. 

RIGHT HAND SPIRAL GEARS. 

In spiral gearing the wheels have cylindrical pitch surfaces, 
but the teeth are not parallel to the axis. The line in which 
the pitch surface intersects the face of a tooth is part of a 
screw line, or helix, drawn at the pitch surface. A screw 
wheel may have one or any number of teeth. A one-toothed 
wheel corresponds to a one-threaded screw, a many-toothed 
wheel to a many-threaded screw. The axes may be placed at 
any angle. 

Consider spiral gears with : 

I. Axes parallel. 
II. Axes at right angles. 
III. Axes any angle. 



3° 



BROWN & SHARPE MFG. CO. 




Fig. 10. 

LEFT HAND SPIRAL GEAR. 

Let there be : 

N°= \ numDer °f teeth in gears \ a , 

C = center distance. 

P' = circular pitch (circumferential not axial). 
P n = normal diametral pitch. 
P' w = normal circular pitch. 

y = angle of axes. 

L, = exact lead of spiral on pitch surface. 
L a = approximate lead of spiral on pitch surface. 

T = number of teeth marked on cutter to be used when 
teeth are to be cut on milling machine. 

D = pitch diameter. 

B = blank diameter. 

° Z [■ angle of teeth with axis 

/ = thickness of tooth. 
s = addendum and module. 
D" + / = whole depth of tooth. 

Note.— Letters a and b occurring at bottom of notations refer to gears a and b. 

I. — Axes Parallel. 
Gears of this class are called twisted gears. The angle of 
teeth with axes in both gears must be equal and the spirals 
run in opposite directions. The angles are generally chosen 
small (seldom over 20 ) to avoid excessive end thrust. End 
thrust may, however, be entirely avoided by combining two 
pairs of wheels with right and left-hand obliquity. Gears of 
this class are known as Herringbone gears. They are com- 
paratively noiseless running at high speed. 



BROWN & SHARPE MFG. CO. 31 

II. — Axes at Right Angles. 
Here we must always have : 

1. The teeth of same hand spiral ; 

2. The normal pitches equal in both gears ; and 

3. The sum of the angles of teeth with axes = 90 . 

Choosing Angle of Teeth with Axes. 

1. If in a pair of gears the ratio of the number of teeth is 
equal to the direct ratio of the diameters, 1. e., if the number of 
teeth in the two gears are to each other as their pitch diame- 
ters, then the angles of the spirals will be 45 ° and 45 ° ; for, this 
condition being fulfilled, the circular pitches of the two gears 
must be alike, which is only possible with angles of. 45 °. In 
such a combination either gear may be the driver. 

2. If the ratio of the diameters determined upon is larger 
or smaller than the ratio of the number of teeth, then the 
angles are : 

In such gears the velocity ratio is measured by the number 
of teeth, and not by the diameters. 

3. Given N a , N 6 and C : 

If P ' is made = P 6 ', then we have case " 1 " and 

ry __ 71 C 



^(N„+N t ) 
But if P„' is assumed, then : 

p , Cn-}£ N a P a ' 

and 

P ' P ' 

tan<r a =*£ tan *» = -*-, 

The gear whose P' or a is larger will ordinarily be the 
driver, on account of the greater obliquity of the teeth. 

4. Given N a , N b and C or D. 
See case " 7 " under III., considering ;/ = 90 . 

III. — Axis at any Angle (y). 

5. Given case " 1," under II., then angles of spirals = }& y f 
for the same reason. 

6. Analogous cases to "2" and "3," under II., may be 
worked out, when angles of axes = y % but they have been 



3 2 



BROWN & SHARPE MFG. CO. 



omitted, partly because the formulas are too cumbersome, and 
partly because they are to some extent covered by cases " 5 " 
and " 7." 

7. Given N , N 6 and C, or one of the pitch diameters. We 
find the angles by a graphic method, which for all practical 
purposes is accurate enough ; ro and v are the axes of gears 
forming angle y (see diagram, Fig. 11.) On these axes we 
lay off . lines r and o v representing the ratio of the number 
of teeth (velocity ratio), so that N : N b : : r s : s v, and 




Fig. 11. 



construct parallelogram r s v. Then, according to Mc- 
Cord,* the angles formed by the tangent s in the pitch con- 
tact with the axes of the gears insures the least amount of 
sliding. In bisecting angle y by tangent u and using angles 
produced in. this manner we equally distribute the end thrust on 
both shafts. Both methods have their advantages ; to profit 
by both we select angles a a and a hy produced by tangent o x, 
bisecting angle u s. 

Thus we have when angles are found and C given, 
2 C n cos a a cos «J 



p>» 



and when D given 



N a cos a b + N b cos a a 



pm = D a ^cosar a and 



D„ = 



P' W N 6 
n cos a b 



* McCord, Kinematics, page 278. 



brown & sharpe mfg. co. 33 

General Formulas. 



y = a a + a b 




p 9n p m 




it it cos a 


B = D + 2j or = 


= D + i 


N cos a 


P' w = P' cos a 




P w = -^ (Pitch of cutter.) 


pm x 

'"7 or = P^ 




2 




D" + /= 2 i + - 

10 




T _ N 
cos 8 a 


(&* jV*/** /.) 


NP' or N* of {Lu = N.F. 
' tan a P tan a I Ln, = N t F. 


T io W G, 
L « SG. 


(£«?«? Note 2 and examples?) 



I cos 45° = .70711 \ 

cos 3 45° = .3535 
\tan 45°= 1.000 / 

Note i. — Cutters of regular involute system. 

Use No. 1 cutter for T from 135 up. 1 No. 5 cu 

u 2 44 tt tt it 55 to 134 " 6 

a 3 .« ** «. 4, 3S to 54 " 7 

" 4 «* " " «• 26 to 34 I " 8 

Note 2. — Gears used on spiral head and bed for Brown & Sharpe milling; 
machine : 

W = number of teeth in gear on worm. 
Gi = " •• 1st " stud. 

Gta " u ad " stud. 

S= •• " u screw. 

Should a spiral head of different construction be used, the formula might not 
apply. 



For 


T 1 


from 


ai to 35 


ti 


4t 


ti 


17 to 30 


44 


(4 


44 


14 to 16 


tt 


(4 


4t 


13 tO 13 



34 



BROWN & SHARPE MFG. CO. 



The following data are usually required in cutting spiral 
gears in a Universal Milling Machine, and it will be found 
convenient to arrange them in tabular form as follows : 





GEAR. 


PINION. 




_. . 




xH o. oi iccm --------- 




± inn L/iamcicr --------- 

Outside Diameter 




v^iriuicir a inn --------- 

Angle of Teeth with Axis 

Normal Circular Pitch 

Pifrrh r»f Pntfpr- -------- 




IT 1LLI1 OI V^ULICI" -------- 




^xUUCIlUUIIl o --------- 

Thickness of Tooth t 

Whole Depth D"+f 

No. of Cutter 

Exact Lead of Spiral 

Approximate Lead of Spiral - - - - 




Gears on Milling Machine to Cut Spiral 

Gear on Worm 

ist Gear on Stud 

2nd Gear on Stud 

Gear on Screw 





If the exact lead L x can be obtained by the gears at hand, 

Li will equal L 2 and we shall have from the formula 

_ 10 W G 2 
L 2 — 



10 

Example I. 



S Gi 
W G 2 



c~~q~ (for B. & S. Milling Machine.) 



Required the gears for cutting a spiral of 2%" lead. 

2\ I 

— == -■ factoring, in the most simple way, we have 



i 
4 



4 
i X I 



2X2 



I X 28 
56 X 2 



32 X 28 
56 X 64 



W G, 
S d 



BROWN & SHARPK MFG. CO. 35 

Thus the gearing will be 32 T. on worm, 64 T. 1st, on stud, 
28 T. 2nd on stud, and 56 T. on screw. 

Trying these gears on the Milling Machine we find that 
they cannot be used, and as we have no other regular gears 
in the ratio of 2 to 1 that can be used we must try, by factor- 
ing, to get such ratios for the two pairs of gears as to be able 
to use the gears at hand, bearing in mind that the combined 
ratio must be J. 

I_ I? _ 3 x 6 _ 24 x 6 24 x 48 
4 ~~ 72 — 9x8 — 9x64" 72x64 

These gears are at hand and the combination can be used 
on the machine, giving the exact lead of 2%". 

Example II. 

Required the gears for cutting a spiral of 8.639" lead. 

8.639 = 8 t 6 d 3 tht ; reducing, by continued fractions, to a 
smaller fraction of approximately the same value, as described 
on pages 50 and 5 1 



639 ) 1000 ( 1 
639 

36i ) 639 ( 1 
36i 

278 ) 361 ( 1 
278 

~83~) 278 ( 3 
249 

29 ) 83 ( 2 
58 
25 ) 29 ( 1 

25 

4)25(6 
24 

1 )4(4 
4 



36 BROWN & SHARPE MFG. CO. 



+ t 1 a h h m * 



39 



Selecting |£ as an approximation near enough for our 
purpose, and in fact as near as we are likely to find gears for, 
we have for our lead 8ff . Applying the formula as in Ex- 
ample I. 



10 


W G* 
S G, 


*H 


216 108 


10 


250 — 125 


9 x 12 


9x48 



factoring we have 

isTt = ^Ts = ^55H5 the S ears ™q«i«*l. 

these being regular gears furnished with the Milling Machine. 

Proof: 

72 x 48 X 10 = 

.001" error in lead. 

In shops where much work is done in milling spirals it is 
desirable to have a full set of gears for the milling machine, 
from the smallest to the largest numbers of teeth that can be 
used. This makes it possible, in most cases, to get closer 
approximations than could be otherwise obtained, and often 
saves a great deal of figuring. 

When the use of continued fractions does not bring a 
close enough approximation, one method to secure a closer 
result is to add to or substract from the numerator and de- 
nominator of the fraction to be reduced, any numbers nearly 
in proportion to the given fraction, seeing that the numbers 
added or substracted are such as to make the fraction reduc- 
ible to lower terms. By a little ingenuity and patience ex- 
tremely close approximations can generally be reached in 
this way. 

Take, as an illustration, the fraction in Example II. 

8tM& 8639 



10 IOOOO 

Adding 9 to the numerator and 10 to the denominator, these 



BROWN & SHARPS MFG. CO. 37 

being in about the same ratio to each other as the numerator 
and denominator of the fraction, we have 

8639+9 = 8648 _ 4324 _ 47 x 92 
10000+10 = 10010 5005 55 x 91 

All of the gears in this case are special. 

Applying the same proof as in Example II. we find that 
this train of gears will give a lead of 8.6393 +, making an 
error of .0003" in the lead. 

No doubt a much closer approximation even than this 
could be obtained by further trial. 

Another method is to multiply both terms of the fraction 
by some number which will make one term of the fraction 
easily reducible, and adding one to or subtracting it from the 
other term to make it possible to reduce that also. 

There is an element of uncertainty in both these methods, 
as we never feel sure that we have obtained the best combina- 
tion ; practical work, however, rarely requires accuracy beyond 
a point that can readily be reached. 

The tables of prime numbers and factors, pages 121 to 
155, will be found convenient in reducing and factoring' 
fractions. These tables are condensed as much as possible 
and give all numbers from 1 to 10,200. 



CHAPTER VI. 

INTERNAL GEARING. 

PART A.— INTERNAL SPUR GEARING. 
(Figs. 12, 13, 14, X5, 16.) 

A little consideration will show that a tooth of an internal 
or annular gear is the same as the space of a spur — external 
gear. 

The epicycloidal form of tooth is preferable for internal 
gears, as there is less difficulty in overcoming the inter- 
ferences. The involute form of tooth can be used by 
changing the pressure angle beyond the limit of inter- 
ference. Special constructions are required when the differ- 
ence between the number of teeth in gear and pinion is 
small. 

In using the system of epicycloidal form of tooth in 
which the gear of 1 5 teeth has radial flanks, this difference 
must be at least 15 teeth, if the teeth have both faces and 
flanks. Gears fulfilling this condition present no difficulties. 
Their pitch diameters are found as in regular spur gears, and 
the inside diameter is equal to the pitch diameter, less twice 
the addendum. 

If, however, this difference is less than 15, say 6, or 2, or 1, 
then we may construct the tooth outline (based on the epicy- 
cloidal system) in two different ways. 

First Method. — To explain this method better, let us sup- 
pose the case as in Fig. 12,. in which the difference between 
gear and pinion is more than 15 teeth. Here the point o of 
the describing circle B (the diameter of which in the best 
practice of the present day is equal to the pitch radius of a 15 
tooth gear, of the same pitch as the gears in question) gene- 
rates the cycloid o, o 1 , o a , o*, etc., when rolling on pitch circle 
L L of gear, forming the face of tooth ; and when rolling on 
the outside of L L the flank of the tooth. In like manner is the 
face and flank of the pinion tooth produced by B rolling out- 
side and inside of E E (pitch circle of pinion). A little study 



BROWN & SHARPE MFG. CO. 



39 



of Fig. 12 (in which the face and flank of a gear tooth are 
produced) will show the describing circle B divided into 12 




equal parts and circles laid through these points* (1, 2, 3, etc.), 
concentric with L L. We now lay off on L L the distances 
0-1, 1-2, 2-3, etc., of the circumference of B, and obtain points 



40 BROWN & SHARPE MFG. CO. 

r S *\ 3 1 ) etc. [Ordinarily it is sufficient to use the chord.] It 
will now readily be seen that B in rolling on L L will success- 
ively come in contact with i', 2 1 , 3 1 , etc., c meanwhile moving 
to c\ c 9 , c*, etc. (points on radii through i 1 , 2 1 , 3 1 , etc.), and the 
generating point o advancing to o 1 , o 2 , o*, etc., being the inter- 
sections of B with c\ c*, e* y etc., as centers and the circles laid 
through 1, 2, 3, etc. Points o, o 1 , o 2 , o*, etc., connected with a 
curve give the face of the tooth ; in like manner the flank is 
obtained. 

In this manner the form of tooth is obtained, when the 
difference of teeth in gear and pinion is less than 15, with the 
exception that the diameter of describing circle B 



= *(£^ b ) 



where P = diametral pitch, Na and Nb number of teeth in 
gears. 

The distances of the tooth above and below the pitch line 
as well as the thickness / are determined as in regular spur 
gears by the pitch, except when the difference in gear and 
pinion is very small, where we obtain a short tooth, as in Figs. 
13 and 14. In such a case the height of tooth is arbitrary and 
only conditioned by the curve. In internal gears it is best to 
allow more clearance at bottom of tooth than in ordinary spur 
gears. 



29 Teeth 



—B 



42 T. 



8 P. 
30 Teeth 




Fig. 13. 



In a construction of this kind it is suggested to draw the 
tooth outline many times full size and reduce by photography. 
An equally multiplied line A B will help in reducing. 



BROWN & SHARPE MFG. CO. 



41 




42 BROWN & SHARPE MFG. CO. 

Second Method. — The difference between gear and pinion 
being very small, it is sometimes desirable to obtain a smooth 
action by avoiding what is termed the " friction of approach- 
ing action."* This is done, the pinion driving , by giving gear 
only flanks, Fig. 15, and the gear driving ; by giving gear only 
faces, Fig. 16. In both these cases we have but one describ- 
ing circle, whose diameter is equal to the difference of the two 
pitch diameters. The construction of the curve is precisely 
the same as described under A. The describing circle has 
been divided into 24 parts simply for the sake of greater 
accuracy. 



PART B.— INTERNAL BEVEL GEARS. 

(Fig. 17.) 

The pitch surfaces of bevel gears are cones whose apexes 
are at a common point, rolling upon each other. The tooth 
forms for any given pair of bevel gears are the same as for a 
pair of spur gears (of same pitch) whose pitch radii are equal to 
the respective apex distances of the normal cones (/. <?., cones 
whose elements are perpendicular upon the elements of the 
bevel gear pitch cones). (Compare Fig 19, page 45.) 

The same is true of internal bevel gears, with the modifica- 
tion that here one of the pitch cones rolls inside of the other. 
The spur gears to whose tooth forms the forms of the bevel 
gear teeth correspond, resolve themselves into internal spur 
gears (Fig. 17). The problem is now to be solved as indicated 
in the first part of this chapter. 



* McCord, Kinematics, pages 107, 108 v 



BROWN & SHARPE MFG. CO. 



43 



Genr 40 Trrtft 
Pinion 20 Teeth 




Fig. 17. 



CHAPTER VII. 

DIMENSIONS AND FORM FOR BEVEL GEAR 

CUTTERS. 

(Fig. 19.) 

The data needed to determine the form and thickness of a 
bevel gear cutter are the following : 
P = pitch. 

Na= number of teeth in gear. 
Nb = number of teeth in pinion. 
F = length of face of tooth, measured on pitch line. 
After having laid out a diagram of the pitch cones a b c and 
a bf y and laid off the width of face, the problem resolves itself 
into two parts : 

Part I.— Determine Proper Curve for Cutter. 
It will be remembered that in the involute system of cutters 
(the only one used for bevel gears that are cut with rotary 
cutter), a set of eight different cutters is made for each 
pitch, numbering from No. 1 to No. 8, and cutting from 
a rack to 12 teeth. Each number represents the form of 
a cutter suitable to cut the indicated number of teeth. For 
instance, No. 4 cutter (No. 4 curve) will cut 26 to 34 teeth. 
In order to find the curve to be used for gear and pinion 
we simply construct the normal pitch cones by erecting 
the perpendicular p q through b, Fig. 19. We now measure the 
lines b q and bp, and taking them as radii, multiplying each by 
2 and P we obtain a number of teeth for which cutters of 
proper curves may be selected. From example we have : 

Gear : b q r= 9^" ; 2 X P X 9.75 = 98 T No. 2 curve. 
Pinion: bp = 3^" ; 2 X P X 3-5 — 35 T No. 3 curve. 
The eight cutters which are made in the involute system 
for each pitch are as follows : 

No. 1 will cut wheels from 135 teeth to a rack. 

" 134 teeth. 
" 54 
" 34 
" 25 
" 20 " 
" 16 " 
" 13 



2 4 


1 « 


a 


55 


3 


i u 


u 


35 


4 ' 


< u 


u 


26 


5 * 


< a 


u 


21 


6 


1 u 


a 


17 


7 


1 u 


a 


14 


8 


t a 


u 


12 



BROWN & SHARPS MFG. CO. 



45 




46 BROWN &. SHARPE MFG. CO. 

Part II.— Determine Thickness of Cutter. 

It is very evident that a bevel gear cutter cannot be thicker 
than the width of the space at small end of tooth ; the practice 
is to make cutter .005" thinner. Theoretically the cutting angle 
{h) is equal to pitch angle less angle of bottom (or A = a — /?'). 
Practically, however, better results are obtained by making 
h = a — fl (substituting angle of top for angle of bottom), and 
in calculating the depth at small end, to add the full clearance 
(/) to the obtained working depth, giving equal amount of 
clearance at large and small end. This is done to obtain a 
tooth thinner at the top and more curved. As the small end 
of tooth determines the thickness of cutter, we shall have to 
find the tooth part values at small end. From the diagram it 
will be seen that the values at large end are to those at small 
end as their respective apex distances (a b and a I). The 
numerical values of these can be taken from the diagram and 
the quotient of the larger in the smaller is the constant where- 
with to multiply the tooth values at large end, to obtain those 
at small end. In our example we find : 

For 5 P we have : 



a I = 3.8 
«J = 5 .8 


•655 = 


= constant 


'=•3141 






t - .2057 


s = .2000 






/=r.I3IO 


/=.03i4 






/«.o3i4 


*+/=.23i4 




/ 


+ /=.i624 


»"+/ = .43i4. 






/«..T3io 






D'" 


+ /=-2934 



From the foregoing it is evident that a spur gear cutter 
could not be used, since a bevel gear cutter must be thinner. 

If in gears of more than 30 teeth the faces are proportion- 
ately long, we select a cutter whose curve corresponds to the 
midway section of the tooth. The curve of the cutter is found 
by the method explained in Part I. of this Chapter. 



BROWN A SHARPE MFG. CO. 4* 

PART III.- SELECTION OF CUTTERS. 
The tables, pages 94 and 95, are convenient for selecting 
cutters for cutting bevel gears and are those used in furnish- 
ing cutters from stock. The various numbers of teeth in 
gear and pinion are given and at the intersection of the two 
columns will be found the numbers of cutter required. 

Example — Required cutters for a pair of bevel gears, 
8 pitch; gear 24 teeth, pinion 12 teeth. 

In column at left of table, page 94 will be found 24 
teeth and in column at top 12 teeth; at the intersection 
of these two columns is found the number of the cutters, in 
this case No. 3 for the gear and No. 8 for the pinion. 
teeth^t he Different methods are employed to compromise in the 
thesma cu ttingf of a bevel gear. When a blank is rotated in adjust- 
ing to finish the large end of the teeth, there need not be 
much filing of the small end, if the cutter is right, for a given 
pitch circle, but the tooth faces may be rather thin at the 
large ends. This compromise is usually preferred, as it 
does not require much filing of the teeth ; it is the same as 
given . in the general catalogue issued by Brown & Sharpe 
Mfg. Co. and is used, by them to fill any order for bevel 
5f lec tt°r £ ear cutters » unless the number of the cutter is specified in 
AT^tobe^ ^he OI "der. This means that a customer would receive a No. 
filed. g^ g_pit c h bevel gear cutter in reply to an order for a 
cutter to cut a 12-tooth pinion, *4" face, while in their 
own gear cutting department the same pinion might be 
cut with a No. 6, 8-pitch cutter, because it is pre- 
ferred to file the teeth at the small end after cutting 
them to the right thickness at the faces of the large end. 
No. 6 instead of a No. 8 would be taken only for a 12-tooth 
pinion that is to run with a gear two or three times as 
large. In the gear cutting department of Brown & Sharpe 
Mfg. Co. it is the general practice to step off to the next 
cutter for pinions fewer than 25 teeth, when the number for 
the teeth has a fraction nearly reaching the range of the 
next cutter: thus, if twice the back cone radius in inches, 
multiplied by the diametral pitch, equals 20.9, a No. 5 
cutter should be used, which is for 21 to 25 teeth inclusive. 
In filling an order for a gear cutter, the fraction is not con- 
sidered, but the cutter indicated by the whole number is 
sent. 



48 



BROWN A SHARPE MFG. CO. 



PART IV.— SELECTING CUTTERS BY USE OF BACK CONE RADIUS. 




Measure the back cone radius a b for the gear, or b c for 
the pinion. This is equal to the radius of a spur gear, the 
number of teeth in which would determine the cutter to use. 

RULE. — Multiply the back cone radius by 2 and the 
product by the diametral pitch ; the resulting product is the 
number of teeth for which to select the cutter. 

Example. — Let the back cone radius a b = 4" and the 
diametral pitch = 8. 2 X 4 = 8, 8 X 8 = 64, the number 
of teeth for which the cutter should be selected, which in 
this case would be a No. 2 Cutter. 



CHAPTER VIII. 

THE INDEXING OF ANY WHOLE OR FRACTIONAL NUMBER 
—DIFFERENTIAL INDEXING. 

(Fig. 21 ) 




-Change Gear 

Fig. 21. 



In indexing on a machine the question simply is : How 
many divisions of the machine index have to be advanced to 
advance a unit division of the number required. To which 
is the 

divisions of machine index 



answer = 



number to be indexed 



Suppose the number of divisions in index wheel of machine 
to be 216. 

Example I. — Index 72. 

Answer: 216 , . c x 

— = 3 (3 turns of worm). 
72 



5° 



BROWN & SHARPE MFG. CO. 



Example II. — Index 123. 

2 i* = 1 + J>3 
123 123 

If now we should put on worm shaft a change gear having 
123 teeth, give the worm shaft, Fig. 21, one turn, and in addi- 
tion thereto advance 93 teeth of the change gear (to give the 
fractional turn), we would have indexed correctly one unit of 
the given number, and so solved the problem. Should we not 
have change gear 123 we may try those on hand. The ques- 
tion then is : How many teeth (x) of the gear on hand (for 
instance 82) must we advance to obtain a result equal to the 
one when advancing 93 teeth of the 123 tooth gear? We have : 

3A. — , A. where x = 62 
123 82 

Example III. — Index 365, change gear 147. 

— = X where x - 87 - — 

365 147 3 6 5 

Here 147 is the change gear on hand. In indexing for a unit 
of 365 we advance87teeth of our 147 tooth gear. It is evident 
that in so doing we advance too fast and will have indexed 
three teeth of our change gear too many when the circle is 
completed. To avoid having this error show in its total amount 
between the last and the first division, we can distribute the 
error by dropping one tooth at a time at three even intervals. 

Example IV. — Index 190. 

216 __ 26 

7^ — Jj^ Change gear on hand 88 T 

— = £- where x = I2 + — 
190 88 190 

To distribute the error in this case we advance one additional 
tooth ot a time of the change gear at eight even intervals. 

Example V.— Index 117 .3913. 

216 , 986087 



"7-39 x 3 II 739 1 3 

This example is in nowise different from the preceding 
ones, except that the fraction is expressed in large numbers. 
This fraction we can reduce to lower approximate values, 
which for practical purposes are. accurate enough. This is 
done by the method of continued fractions. [For an explana- 



BROWN A SHARPE MFG. CO. 5 1 

tion of this method we refer to our " Practical Treatise on 
Gearing."] 

986087 



"73913 
986087) 1173913 (1 
986087 

i87&6) 986087 (5 
939130 

46957) -878a6 (3 
14087 1 

"46955) 46957 (1 ♦ 
4P955 

2) 46955 (33477 
46954 

1)2(2 

2 

986087 =T 



"73913 , + , 



5 + i 
3 + i 
1 + 1 



23477 + £ 

2 



'=3 1 23477 



rf=ri ^ = 5 d = 16 21 4 93033 9 86087 

rt l =i ^ = 6 </' = 19 25" 586944 1173913 

Note. — Find the first two fractions by reduction » - and — j — = -r ; the 

' 11 1 -t- 1 o 



others are then found by the rule \ ,f^~ a , _ 



The fraction \\ is a good approximation; putting therefore 
a change gear of 25 teeth on worm shaft, we advance (beside 
the one full turn) 21 teeth to index our unit. 

Of course, in using any but the correct fraction we have an 
error every time we index a division ; so that when indexed 
around the whole circle, we have multiplied this error by the 
number of divisions. 

In the present example this error is evidently equal to the 
difference between the correct and the approximate fraction 
used. Reducing both common fractions to decimal fractions 
we have : 

-9 — = .84000006 

"739*3 

21 

2 -- = .84000000 

.00000006 = error in each division. 



5 s 



BROWN & SHARPE MFG. CO. 



.00000006 X 1 1 7.3913 = .00000704348 total error in complete 
circle. This error is expressed in parts of a unit division. (To 
find this error expressed in inches, multiply it by the distance 
between two divisions, measured on the circle.) In this case 
the approximate fraction being smaller than the correct one, 
in indexing the whole circle we fall short .00000704348 of a 
division. 

Example VI.-*-Index 15.708 

216 , 11796 

= 13 + — — 



I5-7Q 8 x 57o8 

"796 „ 983 

15708 1309 

983) 1309(1 
??3 

326) 983 (3 
978 

5)326(65 
30 
26 

D5(5 
5 
o 



2?i = i 



IJ09 



i + I 

3+i 

65 + 1 
5 

3 65 



13 196 983 

1 4 261 1309 



In using the approximation £#f- the error for each division 
(found as above) will be .000002927, for the whole circle 
.0000460. In this case, the approximation being larger than 
the correct fraction, we overreach the circle by the error. 



BROWN A SHARPE MFG. CO. 53 



DIFFERENTIAL INDEXING. 



The gearing of the spiral head spindle of a Milling 
Machine to the index plate is equivalent to increasing the 
spacing numbers of the machine, as the rotation of the index 
plate modifies the movement of the index crank at each 
indexing. 

When this modification is employed, the indexing is 
known as Differential Indexing. 

Usually the regular spacing number of a Milling 
Machine is 40. 

V = number of turns of the index plate to one turn of 
the spindle = the train of gears, either simple or compound 
geared.* 

N = number of divisions required. 

h = number of holes in index plate circle to be used. 

n = number of holes taken at each indexing. 

Then -r- = number of turns of the index crank at each 
n 

indexing in relation to the index plate. 

40 — V = spacing number when the index plate rotates 
in the same direction as the crank, using one idler. 

40 + V = spacing number when the index plate rotates 
in the opposite direction to the crank, using two idlers. 

When compound gearing is employed, the two gears on 

the gear stud act as one idler in relation to the direction that 

the index plate rotates. 

Nn 
— r— = number of turns of the crank in N indexings, when 

plate is held stationary. In ordinary indexing — r— = 40. 



In Differential Indexing, — r— is increased or decreased by 



Nn 
the rotation of the index plate while turning the index 

•That is, V — the product of the driving gears divided by the product of the 
driven gears. The gear on the spiral head spindle and the first gear on the stud are 
drivers ; the second gear on the stud and the gear on the worm are driven. 



54 BROWN A SHARPE MFG. CO. 

crank. -=— denotes in all cases the turns of the crank in 
h 

relation to the index plate. 

V = 40 r— , when using one idler and -7— is less 

than 40. 

Nn , . . „ , Nn . 

V = — r 40, when using two idlers and — r— is greater 

than 40. 

40 -v h 

N = n or N = (40 — V) — , using one idler. 

TT n 

40 + v h 

N = n or N = (40 + V) — , using two idlers. 

IT 

To figure a table of different divisions, N, it is convenient 
to assume various ratios, V, and find divisions obtainable 
from the spacing numbers 40 — V and 40 + V. Assuming 

different values for -r-. 
n 

Assuming V = 1 , 40 — V = 39, one spacing number, em- 
ploying one idler. With this, divisions can be obtained that 

are composed of any of the factors of 39 divided by -7-, or 

h 
39X-. 

Examples.— Spacing number 39. 

n= 1, h = 5; N = 39X-y- = 195. 

n=i, h = 7; N = 39X-y- = 273. 

n = 3, h=i7; N = 39Xy = 22i 

The other spacing number, when V = 1, is 40 + 1 = 41. 
As 41 is prime, aliquot divisions can be obtained only by 

giving a value of 1 or 41 to n, when -7- is in its lowest terms. 



BROWN A SHARPE MFG. CO. 55 

Examples.— Spacing number 41 . 

49 
n = 1, h = 49. N = 4i X — = 2009. 

n = 4i,h=i7. N = 4iX^-=i7. 

FRACTIONAL SPACING NUMBERS. 

If V is a fraction, the spacing number is fractional. 

2 1 

Assuming V = — , 40 — V= 39 — , one spacing number 

■ji 1 118 
employing one idler. 39 — = . 

Examples.— Spacing number 39 — . 

118 3 
n= 1, h = 3; N = X— = 118. 

IJ 8 3 
n = 2, h = 3 ; N = — X-|-=S9. 

n8 15 
n = 2, h=i5; N=— X-y = 295. . 

2 2 

The other spacing number, when V = — , is 40 + ■ — = 

2 122 
40 — .= , using two idlers. 

2 
Examples. — Spacing number 40 — . 

122 3 
n=i, h = 3; N = -X— =122. 

122 33 
n=i,h = 33; N = — X^-=i 34 2. 

N given to find V; In this case -r- must be assumed. 

n 

The formula, V = 40 =— or V = -= 40 can be 

n h 

used in solving for V. First find -r- that will give a number 
of divisions approximating N; this assumed number is - — . 



c6 BROWN & SHARPE MFG. CO. 

Example i. 

N = 59. Required -7- and V. 

n 40 2 

Try -7- for 60 divisions = -?— = — . In this case 
7 h 60 3 

Nn 59 X 2 1 , , _ 

— : — = = 39 — , which is less than 40 and the formula 

h 3 oy - 3 * 

, 7 Nn . 

V = 40 r— is used. 

59 X 2 2 
40 — — , therefore in 59 indexings the crank 

2 
will still require — of a turn to complete the 40 necessary 

2 
for one revolution of the spindle : The train or V = — 

v 3 

2 
and the gear on the spindle must have — the number of 

teeth in the gear on the worm, using one idler. 

Example 2. 

N = 319. Required -r- and V. 

Try -=— for 290 divisions = - — . 
7 h * 29 

Nn 
In this case —7— is greater than 40 and using the formula 

v Nn ■ 

V = nr - 4 o. 

319X4 

40 = 4. V = 4 and the index plate must 

29 

turn in the opposite direction to the crank. 

When the ratio is not obtainable with simple gearing, it 

can sometimes be obtained with compound gearing. 

— can be expressed as follows: — — — or — — - for 

1 r 1 X 3 24 X 48 

which there are available gears. 



BROWN & SHARPE MFG. CO. 57 

When the assumed number is less than N, the formulas 

,r Nn 

V = —r 40 can also be expressed in the form : 

V = -£- (N — ^-) and when greater than N, V = 40 — — 

n • n h 

can be expressed V = -r- ( N). 

These formulas indicate that the gear ratio, V, can be 
obtained by multiplying the indexing, — f by the difference 

between the assumed number, , and the required num- 
ber, N. 

Spacing for quarter degrees. 

Example 3. — Required -r- and V for spacing — degree 
or 1440 divisions. 

Try— = — and the assumed number is 1320. 

V = n 40h. _ 1 ^120 
-r-(N —' — -IT (I440— I320) = . 

h n 33 33 

__ 120 64 X 100 

7T ° r 40X 44' 
Two idlers are required, one in addition to the gears on 
the compound gear stud. 

ALIQUANT OR FRACTIONAL SPACING. 

EXAMPLE. — Required a Vernier to read to — degree 
or 5 minutes the scale being divided to degrees. 

Each Vernier space can equal — degree. 

11 1 II 4320 8 

7I X 36? = ^ or IT spaces in whole circle = 392 TT 

spaces. 

A n 1 4oh 

Assume -=— = — or = 360. 

h 9 n J 



58 BROWN & SHARPE MFG. CO. 

I 8 I 360 40 64 X IOO 



v = T (392 T7- 36o) = T 



x 



9 v J ^ 11 J/ 9 11 11 40X44* 

One idler in addition to the gears on the compound stud is 
necessary. 

If h contains a factor that is not found in the gears, V 
cannot usually be obtained, unless the factor is cancelled 
by the difference between N and the assumed number or 
unless N contains the factor. 

The index tables furnished with the Brown & Sharpe 
Universal Milling Machines give all divisions from 1 to 382. 
These divisions can all be obtained with the index change 
gears furnished with the machine. Divisions greater than 
382 can be calculated and with additional gears the number 
of obtainable divisions greatly increased. 

This method of indexing is covered by a patent controlled 
by Brown & Sharpe Mfg. Co. 



CHAPTER IX. 

THE GEARING OF LATHES FOR SCREW 
CUTTING. 

(Figs. 22, 23.) 

The problem of cutting a screw on a lathe resolves itself into 
connecting the lathe spindle with the lead screw by a train of 
gears in such a manner that the carriage (which is actuated by 




Simple Gearing. 

Fig. 22. 



6o 



BROWN &^HARPK MFG. CO. 



the lead screw) advances just one inch, or some definite dis- 
tance, while the lathe spindle makes a number of revolutions 
equal to the number of threads to be cut per inch. 

The lead screw has, with the exception of a very few cases, 
always a single thread, and to advance the carriage one inch it 
therefore makes a number of revolutions equal to its number 




Compound Gearing. 

Fig. 23. 



of threads per inch. Should the lead screw have double 
thread, it will, to accomplish the same result, make a number 
of revolutions equal to half its number of threads per inch. It 
follows that we must know in the first place the number of 
threads per inch on lead screw. 



BROWN & SHARPE MFG. CO. g r 

It ought to be clearly understood that one or more inter- 
mediate gears, which simply transmit the motion received from 
one gear to another, in no wise alter the ultimate ratio of a 
train of gearing. An even number of intermediate gears 
simply change the direction of rotation, an odd number do not 
alter it. 

The gearing of a lathe to solve a problem in screw cutting 
can be accomplished by 

A. Simple gearing. 

B. Compound gearing. 

Referring to the diagrams, Figs. 22 and 23, we have in Fig. 
22 a case of simple, and in Fig. 23 a case of compound gear- 
ing. 

In simple gearing the motion from gear E is transmitted 
either directly to gear Ron lead screw or through the interme- 
diate F. In compound gearing the motion of E is transmitted 
through two gears (G and H) keyed together, revolving on the 
same stud n, by which we can change the velocity ratio of the 
motion while transmitting it from E ,to R. With these four 
variables E, G, H, R, we are enabled to have a wider range of 
changes than in simple gearing. 

B and C, being intermediate gears, are not to be considered. 
If, as is generally the case, gear A equals gear D, we disregard 
them both, simply remembering that gear E (being fast on 
same shaft with D) makes as many revolutions as the spindle. 
Sometimes gear D is twice as large as gear A, then, still con- 
sidering gear E as making as many revolutions as the spindle, 
we deal with the lead screw as having twice as many threads 
per inch as it measures. 



SIMPLE GEARING. 

Let there be : the number of teeth in the different gears 
expressed by their respective letters, as per Fig. 22, and 

s = threads per inch to be cut, 
L = threads per inch on lead screw ; then 
1. s R 

L E 



62 BROWN & SHARPS MFG. CO. 

If now one of the two gears £ and R is selected, the other 
will be: 

R = lF; E = LR 

L s 

2. The two gears may be found by making 

p. ~^ i > where/ may be any number. 

3. The above holds good when a fractional thread is to be 
cut, but if the fraction is expressed in large numbers, as, for 
instance, s = 2.833 ( 2 VWrV)» we ^ TSt reduce this fraction (fffo) to 
lower approximate values by the process of continued fraction 
(see pages 49 and 50). 

833) ICOO (I 

167) 813 (4 
668 

165) 167 (1 
165 

a) 165 (82 
16 







5 

4_ 

1) 2 (a 

a 






I 


4 


I 82 


2 


I 


_4 


_5_ 414 


833 


I 


5 


6 497 


1000 



L = .833 (nearly) and s = 2* 
6 6 

If in this case L = 4, and we select E = 48, then, since 



sE 



R = T R = 34 



COMPOUND GEARING. 



4. In a lathe geared compound for cutting a screw the 
product of the drivers (E and H, Fig. 23) multiplied by the num- 
ber of threads per inch to be cut must equal the product of the 
driven (G and R) multiplied by the number of threads on lead 
screw. This is expressed by 

E . H . s = G . R . L o r ~-^-^ = 1 



BROWN A SHARPE MFG. CO. 6$ 

If three of the gears E, H, G, R have been selected, the 
fourth one would be either 



„ GRL 

E= H s 


or 


„ GRL 


or 


n EH; 
°" KL 


or 


R _EHx 
R GL 




; _RGL _ 


-l( r g 



EH VL.E. 

If a fractional thread is to be cut, as under " 3," we reduce 
the fraction to lower approximate values. 

Example.— Gear for 5.2327 threads per inch, lead screw is 
6 threads. 



.23*7 = ^ 

I OOOO 



2327) iooco (4 

9308 



692) 3327 (3 

2076 

~25~I) 692 (2 

I90) 251 (I 
I90 



6l) 190 (3 
183 

7) 61 (8 
56 



5)7(i 
5_ 

2)5(2 

4 

1)2(2 



43213 8 



13 7 10 37 306 343 99 2 2327 



4 13 3° 43 x 59 13*5 *474 4263 10000 

— = .2327 (nearly) and 5.2327 = $— 
43 43 

Selecting E = 43, H = 52, R = 50, and 

G = E - H - J we have G = *3 ■ * 2 - ffi = - 
R . L 50 . 6 ** 



64 BROWN & SHARPE MFG. CO. 

5. The examples so far given all deal with single thread. 
The pitch of a screw is the distance from center of one thread to 
the center of the next. The lead of a screw is the advance for 
each complete revolution. In a single thread screw the pitch 
is equal to the lead, while in a double thread screw the pitch 
is equal to one-half the lead ; in a triple thread screw equal to 
one-third the lead, etc. 

If we have to gear a lathe for a many-threaded screw 
(double, triple, quadruple, etc.), we simply ascertain the lead, 
and deal with the lead as we would with the pitch in a single 
thread screw, i. *., we divide one inch by it, to obtain the num- 
ber of threads for which we have to gear our lathe. 

Example. — Gear for double thread screw, lead = .4654. 
Number of threads per inch to be geared for is : 

-L- = 2.1487 



Lead 4654 
Lead screw is four threads per inch. 
As in previous examples, we reduce the fraction .1487=^^- 
to lower approximate values by the process of continued frac- 
tion. 

From the different values received in the usual way we 
select : 

Ifi = .1487 (nearly) and 2.1487 = 24^ 

We have therefore : 

* = H± 

L = 4 



E=74 
(H= 4 o 



Selecting -J G = 30 
40 

r- E. H. s _ 74 .40. 2i^ _ 

G . L 30 . 4 " 

Note. — In using any but the original fraction we commit an error. This error 
can be found by reducing the approximate fraction used to a decimal fraction, and 
comparing it with the original fraction. In the above example the original fraction is 

.1487 and 
H = . 1 4864 
Error = .00006 inch in lead. 



In cutting a multiple screw, after having cut one 
thread, the question arises how to move the thread tool the 
correct amount for cutting: the next thread. 



BROWN & SHARPE MFG. CO. 



65 



In cutting double, triple, etc., threads, if in simple or com- 
pound gearing the number of teeth in gear E is divisible by 
2, 3, etc., we so divide the teeth ; then leaving the carriage 
at rest we bring gear E out of mesh and move it forward one 
division, whereby the spindle will assume the correct position. 

When E is not divisible we find how many turns (V) of 
gear R are made to each full turn of the spindle. Dividing 
this number by 2 for double, by 3 for triple thread, etc., we 
advance R so many turns and fractions of a turn, being careful 
to leave the spindle at rest. 

For compound gearing : 

y-E.H 
G.R 
When the gear D is twice as large as the gear A (as ex- 
plained in fifth paragraph, page 60.) the formula would be 

v= E - H - 

2 G. R. 

If in simple gearing both E and R are not divisible, one 
remedy would be to gear the lathe compound ; or the face- 
plate may be accurately divided in two, three or more slots, 
and all that is then necessary is to move the dog from one slot 
to another, the carriage remaining stationary. 



Table of Tooth Parts 



68 



BROWN & SHARPE MFG. CO. 



TABLE OF TOOTH PARTS. 



CIRCULAR PITCH IN FIRST COLUMN. 





Threads or 

Teeth per inch 

Linear. 


1 

P 


Thickness of 

Tooth on 
Pitch Line. 


31 


Working Depth 
of Tooth. 


Depth of Space 

below 

Pitch Line. 


1^ 
2 — 


Width of 

Thread-Tool 

at End. 


Width of 
Thread at Top. 


p' 


i" 
p' 


P 


t 


8 


D" 


•+/ 


D"+/ 


P*.31 


P'X.335 


2 


i 

T 


1.5708 


1.0000 


.6366 


1.2732 


.7366 


1.3732 


.6200 


.6700 


If 


8 
16 


1.6755 


.9375 


.5968 


1.1937 


.6906 


1.2874 


.5813 


.6281 


If 


4 
7 


1.7952 


.8750 


.5570 


1.1141 


.6445 


1.2016 


.5425 


.5863 


if 


8 

13 


1.9333 


.8125 


.5173 


1.0345 


.5985 


1.1158 


.5038 


.5444 


if 


2 
3 


2.0944 


.7500 


.4775 


.9549 


.5525 


1.0299 


.4650 


.5025 


ih 


16 
83 


2.1855 


.7187 


.4576 


.9151 


.5294 


.9870 


.4456 


.4816 


if 


IT 


2.2848 


.6875 


.4377 


.8754 


.5064 


.9441 


.4262 


.4606 


if 


3 

4 


2.3562 


.6666 


.4244 


.8488 


.4910 


.9154 


.4133 


.4466 


14 


16 
81 


2.3936 


.6562 


.4178 


.8356 


.4834 


.9012 


.4069 


.4397 


if 


4 
6 


2.5133 


.6250 


.3979 


.7958 


.4604 


.8583 


.3875 


.4188 


14 


16 
15" 


2.6456 


.5937 


.3780 


.7560 


.4374 


.8156 


.3681 


.3978 


if 


8 
8 


2.7925 


.5625 


.3581 


.7162 


.4143 


.7724 


.3488 


.3769 


14 


16 

17" 


2.9568 


.5312 


.3382 


.6764 


.3913 


.7295 


.3294 


.3559 


l 


1 


3.1416 


.5000 


.3183 


.6366 


.3683 


.6866 


.3100 


.3350 




1* 


3.3510 


.4687 


.2984 


.5968 


.3453 


.6437 


.2906 


.3141 


7 
i 


1+ 


3.5904 


.4375 


.2785 


.5570 


.3223 


.6007 


.2713 


.2931 


"if 


1* 


3.8666 


.4062 


.2586 


^.5173 


.2993 


.5579 


.2519 


.2722 


JL 
5 


li- 


3.9270 


.4000 


.2546 


.5092 


.2940 


.5492 


.2480 


.2680 


3 

4 


i± 


4.1888 


.3750 


.2387 


.4775 


.2762 


.5150 


.2325 


.2513 


11 
16 


l* 


4.5696 


.3437 


.2189 


.4377 


.2532 


.4720 


.2131 


.2303 


8 
S 


i+ 


4.7124 


.3333 


.2122 


.4244 


.2455 


.4577 


.2066 


.2233 


5 
8 


i+ 


5.0265 


.3125 


.1989 


.3979 


.2301 


.4291 


.1938 


.2094 


3 
5 


1-1- 


5.2360 


.3000 


.1910 


.3820 


.2210 


.4120 


.1860 


.2010 


-4. 
7 


li 


5.4978 


.2857 


.1819 


.3638 


.2105 


.3923 


.1771 


.1914 


8 
16 


If 


5.5851 


.2812 


.1790 


.3581 


.2071 


.3862 


.1744 


.1884 



BROWN & SHARPE MFG. CO. 



6 9 



TABLE OF TOOTH PARTS.— Continued. 







CIRCULAR 


PITCH 


IS FIRST COLUMN. 






$4 

0* 




1 . 


a 8 

in 


■32 


to 

15 

m 


2 qj 

%'i 


5 


•si • 


P4 

H 
3-8 


P' 


1" 


p 


t 


8 * 


D" 


•+/ 


D^/. 


Pk.3i 


pk.335 


1 
2 


2 


6.2832 


.2500 


.1592 


.3183 


.1842 


.3433 


.1550 


.1675 


4 



2* 


7.0685 


.2222 


.1415 


.2830 


.1637 


.3052 


.1378 


.1489 


7 

16 


2* 


7.1808 


.2187 


.1393 


.2785 


.1611 


.3003 


.1356 


.1466 


S 

7 


2i 


7.3304 


.2143 


.1364 


.2728 


.1578 


.2942 


.1328 


.1436 


8 
5 


2f 


7.8540 


.2000 


.1273 


.2546 


.1473 


.2746 


.1240 


.1340 


3 
8 


2f 


8.3776 


.1875 


.1194 


.2387 


.1381 


.2575 


.1163 


.1256 


4 
11 


2f 


8.6394 


.1818 


.1158 


.2316 


.1340 


.2498 


.1127 


.1218 


1 

T 


3 


9.4248 


.1666 


.1061 


.2122 


.1228 


.2289 


.1033 


.1117 


5 
16 


3| 


10.0531 


.1562 


.0995 


.1989 


.1151 


.2146 


.0969 


.1047 


8 
10 


3i 


10.4719 


.1500 


.0955 


.1910 


.1105 


.2060 


.0930 


.1005 


2 

7 


3i 


10.9956 


.1429 


.0909 


.1819 


.1052 


.1962 


.0886 


.0957 


1 
4 


4 


12.5664 


.1250 


.0796 


.1591 


.0921 


.1716 


.0775 


.0838 


2 
9 


4i 


14.1372 


.1111 


.0707 


.1415 


.0818 


.1526 


.0689 


.0744 


1 
6 


5 


15.7080 


.1000 


.0637 


.1273 


.0737 


.1373 


.0620 


.0670 


3 
16 


5* 


16.7552 


.0937 


.0597 


.1194 


.0690 


.1287 


.0581 


.0628 


2 
11 


6f 


17.2788 


.0909 


.0579 


.1158 


.0670 


.1249 


.0564 


.0609 


1 
6 


6 


18.8496 


.0833 


.0531 


.1061 


.0614 


.1144 


.0517 


.0558 


2 
13 


6* 


20.4203 


.0769 


.0489 


.0978 


.0566 


.1055 


.0477 


.0515 


1 
7 


7 


21.9911 


.0714 


.0455 


.0910 


.0526 


.0981 


.0443 


.0479 


8 
15 


7i 


23.5619 


.0666 


.0425 


.0850 


.0492 


.0917 


.0414 


.0446 


1 
8 


8 


25.1327 


.0625 


.0398 


.0796 


.0460 


.0858 


.0388 


.0419 


1 
9 


9 


28.2743 


.0555 


.0354 


.0707 


.0409 


.0763 


.0344 


.0372 


1 
10 


10 


31.4159 


.0500 


.0318 


.0637 


.0368 


.0687 


.0310 


.0335 


1 
16 


16 


50.2655 


.0312 


.0199 


.0398 


.0230 


.0429 


.0194 


.0209 


1 
SO 


20 


62.8318 


.0250 


.0159 


.0318 


.0184 


.0343 


.0155 


.0167 



70 



BROWN & SHARPE MFG. CO. 



TABLE OF TOOTH PARTS. 



DIAMETRAL PITCH IN FIRST COLUMN. 







Thickness 
of Tooth on 
Pitch Line. 


6 
-"3 


-*» 
' ft . 

bOO 

£*< 


Depth of Space 

below 

Pitch Line. 


3 
ft^s 

M o 


p 


P' 


t 


8 


D" 


«+/. 


D"+/. 


* 


6.2832 


3.1416 


2.0000 


4.0000 


2.3142 


4.3142 


* 


4.1888 


2.0944 


1.3333 


2.6666 


1.5428 


2.8761 


i 


3.1416 


1.5708 


1.0000 


2.0000 


1.1571 


2.1571 


ii 


2.5133 


1.2566 


.8000 


1.6000 


.9257 


1.7257 


i* 


2.0944 


1.0472 


.6666 


1.3333 


.7714 


1.4381 


if 


1.7952 


.8976 


.5714 


1.1429 


.6612 


1.2326 


2 


1.5708 


.7854 


.5000 


1.0000 


.5785 


1.0785 


2i 


1.3963 


.6981 


.4444 


.8868 


.5143 


.9587 


24 


1.2566 


.6283 


.4000 


.8000 


.4628 


.8628 


2| 


1.1424 


.5712 


.3636 


.7273 


.4208 


.7844 


3 


1.0472 


.5236 


.3333 


.6666 


.3857 


.7190 


«* 


.8976 


.4488 


.2857 


.5714 


.3306 


.6163 


4 


.7854 


.3927 


.2500 


.5000 


.2893 


.5393. 


5 


.6283 


.3142 


.2000 


.4000 


.2314 


.4314 


6 


.5236 


.2618 


.1666 


.3333 


.1928 


.3595 


7 


.4488 


.2244 


.1429 


.2857 


.1653 


.3081 


8 


.3927 


.1963 


.1250 


.2500 


.1446 


.2696 


9 


.3491 


.1745 


.1111 


.2222 


.1286 


.2397 


10 


.3142 


.1571 


.1000 


.2000 


.1157 


.2157 


11 


.2856 


.1428 


.0909 


.1818 


.1052 


.1961 


12 


.2618 


.1309 


.0833 


.1666 


.0964 


.1798 


13 


.2417 


.1208 


.0769 


.1538 


.0890 


.1659 


14 


.2244 


.1122 


.0714 


.1429 


.0826 


.1541 



BROWN & SHARPE MFG. CO. 



7 1 



TABLE OF TOOTH PARTS— Continued. 



DIAMETRAL PITCH IN FIRST COLUMN. 



Is 




Thickness 
of Tooth on 
Pitch Line. 


51 


o 
bOo 
.SH 


Depth of Space 

below 

Pitch Line. 


9*A 


p. 


P'. 


t. 


8. 


D". 


«+/. 


D"+/. 


15 


.2094 


.1047 


.0666 


.1333 


.0771 


.1438 


16 


.1963 


.0982 


.0625 


.1250 


.0723 


.1348 


17 


.1848 


.0924 


.0588 


.1176 


.0681 


.1269 


18 


.1745 


.0873 


.0555 


.1111 


.0643 


.1198 


19 


.1653 


.0827 


.0526 


.1053 


.0609 


.1135 


20 


.1571 


.0785 


.0500 


.1000 


.0579 


.1079 


22 


.1428 


.0714 


' .0455 


.0909 


.0526 


.0980 


24 


.1309 


.0654 


.0417 


.0833 


.0482 


.0898 


26 


.1208 


.0604 


.0385 


.0769 


.0445 


.0829 


28 


.1122 


.0561 


.0357 


.0714 


.0413 


.0770 


30 


.1047 


.0524 


.0333 


.0666 


.0386 


.0719 


32 


.0982 


.0491 


.0312 


.0625 


.0362 


.0674 


34 


.0924 


.0462 


.0294 


.0588 


.0340 


.0634 


36 


.0873 


.0436 


.0278 


.0555 


.0321 


.0599 


38 


.0827 


.0413 


.0263 


.0526 


.0304 


.0568 


40 


.0785 


.0393 


.0250 


.0500 


.0289 


.0539 


42 


.0748 


.0374 


.0238 


.0476 


.0275 


.0514 


44 


.0714 


.0357 


.0227 


.0455 


.0263 


.0490 


46 


,0683 


.0341 


.0217 


.0435 


.0252 


.0469 


48 


.0654 


.0327 


.0208 


.0417 


.0241 


.0449 


50 


.0628 


.0314 


.0200 


.0400 


.0231 


.0431 


56 


.0561 


.0280 


.0178 


.0357 


.0207 


.0385 


60 


.0524 


.0262 


.0166 


.0333 


.0193 


.0360 



Tables Giving Corrected T and 
Corrected S 



74 



BROWN & SHARPE MFG. CO. 



TABLES GIVING CORRECTED T AND CORRECTED S 
FOR GEAR TEETH 

To obtain corrected S and corrected T for any diametral 
pitch divide the corresponding dimension for i diametral 
pitch by the required diametral pitch. 

Example — Find the corrected S and T for a gear 5 
diametral pitch 23 T. 

1. 5 696 -=-5 =.3 1 39 Corrected T 

1.0268-^-5=. 2054 " S 



For 



1 DIAMETRAL PITCH 


No. of 
Teeth. 


No. of 
Cutter. 


Corrected 
T 


Corrected 

S 


8 








9 








IO 








II 








12 


8 


I-5663 


I.05 14 


*3 


7* 


I.5670 


I.0474 


H 


7 


I-5675 


1 .0440 


15 


6* 


!-5679 


I.04H 


l 7 


6 


1.5686 


I.0362 


19 


Si' 


1.5690 


I.0324 


21 


5 


1.5694 


I.0294 


23 


4* 


1.5696 


I.0268 


26 


4 


1.5698 


I.0237 


30 


3* 


1.5701 


I.0208 


35 


3 


1.5702 


I. OI 7.6 


42 


2i 


1-5704 


I.OI47 


55 


2 


1.5766 


I.OII2 


80 


I* 


15707 


I.OO77 


i35 


I 


1.5708 


I.OO46 


table gi< 


ring circu 


lar pitch see f 


ollowing page 



BROWN A SHARPE MFG. CO. 



75 



To obtain corrected S and corrected T for any circular 
pitch, multiply the corresponding dimension for I circular 
pitch by the required circular pitch. 

Example — Find the corrected S and T for a ffl circular 
pitch gear with 1 5 teeth. 

.4991 X ^=.3743 Corrected T 
•33 I 4X^ = .2 4 86 " S 



1 CIRCULAR PITCH 


No. of 
Teeth 


No. of 
Cutter 


Corrected 
T 


Corrected 

S. 


8 








9 








IO 








II 








12 


8 


.4986 


•3347 


13 


7* 


.4988 


•3334 


H 


7 


.4990 


•3323 


15 


6* 


•499 1 


•33 * 4 


i7 


6 


•4993 


.3298 


19 


5* 


•4995 


.3286 


21 


5 


.4996 


•3277 


23 


4* 


•4997 


.3268 


26 


4 ' 


•4997 


.3258 


30 


3* 


.4998 


•3249 


35 


3 


.4998 


•3239 


4 2 


2h 


•4999 


.3230 


55 


2 


.5000 


.3219 


80 


II 


.5000 


.3208 


135 


I 


.5000 


.3198 



Page 77. 



To use these tables for finding the outside diameters of Bevel 
Gears with axes at right angles, divide the figures given opposite 
the required numbers of teeth by the pitch (P) and add to the pitch 
diameter, using the upper figure in the space for the gear and the 
lower for the pinion. 

Thus, for a pair of bevel gears with 24 and 14 teeth 10 P., 
divide 1.01 by 10 = .101 and add to the pitch diameter of the 
gear; 2.40 4- .101 = 2.501, the outside diameter of gear. Divide 
1.73 by 10 = .173 and add to the pitch diameter of the pinion 
1.40 + .173 = 1.573, the outside diameter of the pinion. 



Table Giving Diameter Increments 



7» 



BROWN & SHARPE MFG. CO. 



DIAMETER INCREMENT. 

DIAMETER INCREMENT-GEAR 







26 


25 


24 


23 


22 


21 


20 


19 


18 


17 


16 


15 


14 


13 


12 




12 


84 

1.82 


.87 
1.80 


.89 
1.79 


•93 
1-77 


.96 
1.76 


•y9 

1-74 


1.03 
' 1.71 


1.07 
1.69 


1. 11 
1.66 


«.*5 
1.63 


1.20 
1.60 


1.25 

1.56 


1.30 
152 


1.36 
1.47 


1.41 
1.41 




13 


.89 
1.79 


.92 
1-77 


•95 
1.76 


.98 
1.74 


,1.02 

1.72 


1.05 
1.70 


1.09 
1.68 


1.13 
1.65 


1.17 
x.62 


1. 21 
A -59 


1.26 
1.55 


131 
I-5X 


x.36 
1.47 


1.41 
1.41 






14 


•95 
1.76 


.98 
x-75 


1. 01 
1-73 


1.04 
1.71 


1.07 
1.69 


Z.II 

1.66 


1.15 
1.64 


1.19 
1.61 


1.23 

1.58 


1.27 
1-54 


1.32 
1.50 


1.36 

1.46 


1.41 
x.41 








15 


I. CO 

1-73 


1.03 
1.71 


1.06 

1.70 


1.09 
1.68 


J.13 
1.65 


1.16 
1.63 


1.20 
1.60 


1.24 
1-57 


1.28 
1.54 


1.32 
1.50 


i.37 
1.46 


1.41 
1.41 








16 


1.05 
1.70 


1.08 
1.68 


1. 11 
1.66 


1.14 
1.64 


1.18 
1.62 


X.21 
1-59 


1.25 
1.56 


1.29 
1.53 


1.33 
1.49 


1-37 
X.46 


1.41 
1.41 






z 
o 
z 
a 


17 


1.09 
1.67 


1. 12 

1.65 


1.16 
1.63 


1.19 
1.61 


1.22 

i-58 


1.26 
i-55 


1.30 
1.52 


1.33 

1.49 


1.37 
1.45 


1.41 
1.41 






18 


1.14 
1.64 


1.17 
1.62 


1.20 
1.60 


1.23 
1-57 


1.27 
i-55 


1.30 
152 


i.34 
1.49 


1.38 
1.45 


1.41 
1.41 








19 


1.18 

1.61 


1.21 
1-59 


1.24 
1-57 


1.27 
1-54 


i-3i 
i-5X 


1-34 
1.48 


1.38 
i.45 


1.4. 
1.41 










20 


1.22 
1-59 


1.25 
1-56 


1.28 
1-54 


I-3I 
I-5I 


i-35 

1.48 


1.38 
1-45 


1.41 
x.41 










21 


1.26 
1.56 


1.29 
1-53 


1.32 
1.50 


1-35 
1.48 


1.38 
1-45 


1.41 
1.41 










22 


1.29 
1-53 


1.32 
1-50 


1-35 
1.47 


1.38 
145 


1.41 
1.41 








23 


1-33 
1.50 


1-35 
1.47 


1.38 
1.44 


1.41 
1.41 










24 


1.36 
1-47 


1-39 
1-44 


1.41 
1.41 










25 


X-39 
1.44 


1.41 
1.41 | 










26 


1.41 
1.41 









For bevel gears with axes at right angles only. 



BROWN d. SHARPE MFG. CO. 



79 



DIAMETER INCREMENT— {Continued) 

DIAMETER INCREMENT-GEAR 







41 


40 


39 


38 


37 


36 


35 


34 


33 


32 


31 


30 


29 


28 


27 




12 


•56 
1.92 


.58 
1.92 


.59 
1.91 


.61 
1. 91 


.63 
1.90 


.63 
1.90 


.65 

1.89 


.67 
1.8S 


.68 
x.88 


.70 
x.87 


.72 

x.87 


.74 
1.86 


.76 
1.85 


•79 
1.84 


.81 
x.83 




13 


.60 
1.91 


.6x 
x.90 


.63 
1.90 


.65 
1.89 


.66 

1.89 


.68 
1.88 


.70 
x.87 


7X 
x.87 


•73 
1.86 


.75 
1.85 


.77 
x.84 


.3o 
1.83 


.82 
1.82 


.84 
181 


.87 
1.80 




14 


.65 
1.89 


.66 
1.89 


.67 

x.88 


.69 
1.88 


.71 
1.87 


.72 
1.86 


.74 
x.86 


•76 
*-85 


.73 
1.84 


.80 
1.83 


.82 
1.82 


.85 
1.81 


.87 
1.80 


.39 
x-79 


.92 

x.78 




15 


.69 

1.88 


.70 
I.87 


.72 

1.87 


.74 
1.86 


•75 
x.85_ 


.77 
1.85 


.79 
1.84 


.81 

l.8j 


.83 
1.82 


.85 
1. 81 


.87 
1.80 


.89 
I..79 


.92 
x.78 


•94 
x.76 


•97 
1.75 




16 


.73 
1.86 


•74 
1.86 


.76 
*** 


.77 

1-85 


.79 

1.84 


.81 
I.83 


.83 
1.82 


•85 
1. 81 


.88 
1.80 


.89 
1.79 


.91 
x.77 


•94 
x.75 


.97 
x.75 


•99 
x.74 


1.02 
172 




17 


•77 
1.85 


•78 
1.84 


•79 
1.83 


.81 

1.83 


.83 

1.82 


.86 
1.81 


.88 
1.80 


.89 
1.79 


.91 
x.77 


•94 

1.76 


.96 
x.75 


•99 
1.74 


I.OI 

1-73 


1.04 
1.71 


1.07 
1.69 




18 


.80 
1.8^ 


.82 
1.8* 


.84 
1.81 


.86 
i.8x 


.88 
1.80 


.89 
1.79 


•9X 
1.78 


•93 
X-77 


•94 
1.76 


.98 
X.74 


I.OI 

1.73 


X.03 
1.72 


x.06 
1.70 


x.08 
1.68 


X.II 

1.66 




19 


.84 
1.81 


.86 
x.81 


.88 
I.80 


.89 
1.79 


.91 
x.78 


.93 
1.77 


•95 
1.76 


•97 
x.75 


•99 

x.73 


1.02 
X.72 


1.04 

1.70 


X.07 
X.69 


I.IO 

1.67 


X.12 
1.66 


1x5 
1.64 




20 


.88 
1.80 


.89 
1.79 


.91 

1.78 


•93 

i.77 


•95 
1.76 


•97 
X.75 


•99 
1.74 


I.OI 

x.72 


1.04 
x.71 


I.06 
1.70 


x.o8 
1.68 


1. II 

x.66 


1.14 

x.64 


1.16 
1.63 


x.19 
x.61 




21 


.91 
1.78 


•93 
1-77 


•94 
1.76 


•97 
1.75 


•99 
1.74 


I.OI 

1.73 


1.03 
1.72 


1.05 
x.70 


1.07 
1.69 


1. 10 
1.67 


1. 12 
1.65 


1. 14 
x.64 


x.17 
1.62 


x.20 
1.60 


1.23 
x.58 




22 


•95 
X.76 


.96 
1-75 


.98 
1.74 


1 .00 
1.73 


1.02 
1.72 


1.04 
I.7I 


J.06 
T.69 


1.09 
x.68 


1. 11 
1.66 


I.I3 
x.65 


i.x6 
1.63 


1. 18 
1.61 


I.2I 
X.59 


1.24 
x.57 


1.26 
x.55 




23 


.98 
1.74 


1. 00 
1-73 


x.01 

1.72 


1.04 
1.71 


1.06 
x.70 


1.08 
x.68 


1. 10 
x.67 


1. 12 
1.66 


I.X4 
x.64 


x.17 
1.62 


1.19 
1.61 


1. 21 
x.59 


X.24 
lm5 l 


1.27 
x.55 


x.30 
152 




24 


1. 01 

1.72 


1.03 
1.71 


1.05 

1.70 


1.07 
1.69 


1.08 
1.68 


1. 11 
1.66 


x.13 

1.65 


1. 15 
1-63 


1.17 
1.62 


1.20 
1.60 


x.23 
x.58 


1.25 
1.56 


1.28 
X.54 


1.30 
1.52 


x.33 
x.49 


z 


25 


1.04 
1.71 


1.06 
1.70 


1.08 

1.68 


X.IO 

1.67 


I.X2 
X.65 


x.»4 
1.64 


1.16 

»4» 


1.18 
x.6x 


1.20 

x.59 


1.23 
x.58 


x.26 
1.56 


x.28 
x.54 


x.3X 
152 


1.33 
x.49 


x.36 
x-47 


g 

z 


26 


1.07 
1.69 


1.09 
x.68 


1. 11 
x.66 


1.13 
1.65 


X.I5 
1.64 


1.17 
1.62 


1.19 
1.61 


x.21 
1-59 


x.24 

x.57 


1.26 
x.55 


x.28 
x.53 


x.3X 
X.5X 


x.34 
1.49 


x.36 
1-47 


*.39 

*.44 


0. 


27 


1. 10 
1.67 


X.X2 

1.66 


1.64 


1.15 
1*1 


1. 18 
X.62 


1.20 
1.60 


1.22 

x.,«>8 


x.24 
1-57 


1.27 
x.54 


x.29 
1-53 


x.3X 
x.5X 


1.34 
x.49 


x.36 
1.46 


r.39 
X.44 


I.4I 
1. 41 




28 


1.13 
1.65 


1.14 

1.64 


1.16 
x.62 


1.19 
1.61 


I. 21 
X.59 


x.23 
1.58 


x.25 
1.56 


1.27 
1-54 


1.29 
x.53 


X.32 
1.5X 


x.34 
1.48 


x.36 

x.46. 


1.99 

x.44 


I.4I 
I.4I 






29 


1.15 
1.63 


1.17 
1.62 


1.19 
1.60 


1.21 
X.59 


1.23 
1.57 


1.26 
x.56 


1.38 
1.54 


1.30 
x.52 


x.32 
x.50 


X.34 
1.48 


x.37 
1.46 


1.39 
1.44 


1.41 
1.41 








30 


x.18 
1.61 


X.2U 
I.60 


1.22 
1-59 


x.24 
1.57 


1.26 
1.55 


x.28 
1.54 


1.30 
x.52 


x.32 
x.50 


x.35 
x.48 


1.37 
1.46 


x.39 
X.44 


Mi 
x.4X 


y- 






31 


1.21 

1.59 


I.23 
1.58 


x.25 

1.57 


x.26 
x.55 


1.28 
X.53 


x.31 
x.51 


x.33 
x.50 


x.35 
x.48 


1.37 
1.46 


1.39 
X.44 


1. 41 
I.4X 








32 


1.23 
1.58 


1.25 
1.56 


1.27 
x.54 


1.29 
X.53 


I.3I 
X.5I 


i.33 
x.50 


x.35 
1.48 


x.37 
1.46 


'x.39 
x.44 


X.4X 
MX 










33 


1-25 
1.56 


1.27 
1-54 


1.29 
1.53 


I.3X 
1.51 


1.33 
X.49 


x.35 
1.48 


x.37 
x.45 


X.39 
t-43 


Ml 
I.4X 










34 


X.28 
1.54 


X.30 
1.52 


x.31 
X.51 


x.33 
1.49 


1.35 
X.48 


1.37 
x.45 


1.39 
1.43 


1.41 
x.41 


it rig 


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35 


1.30 
1.52 


1.32 
1.50 


1.34 
1.49 


X.35 
x.48 


X.38 
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1.39 
x.43 


i.4i 
1.41 


xes £ 






36 


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1.36 
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x.38 
x.45 


X.40 
1.43 


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x.41 


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X.36 
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x.45 


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38 


1.36 
1.47 


1.38 
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I.40 
x.43 


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I.4X 


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41 


Mi 

■iiL 


I 





8o 



BROWN & SHARPE MFG. CO, 



DIAMETER INCREMENT— {Continued) 

DIAMETER INCREMENT-GEAR 







56 


55 


54 


53 


52 


51 


50 


49 


48 


47 


46 


45 


44 


43 


42 




12 


•42 

1.96 


•43 
1-95 


•43 
1.95 


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1.94 


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1.92 




13 


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1-95 


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1.94 


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x.93 


53 

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1.92 


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1.92 


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1.92 


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1.91 


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1.91 




14 


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1.94 


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1.94 


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1.93 


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1.93 


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1.93 


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1-93 


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1.92 


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1.92 


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x.93 


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1.91 


59 
1.91 


.61 
1.91 


.02 
1.90 


.63 
190 




15 


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1-93 


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i-93 


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1.92 


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1.92 


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1.92 


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1.92 


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1.91 


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1.91 


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1. 91 


.62 
1.90 


.63 
1.90 


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x.89 


.66 
1.89 


.67 
1.88 




16 


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1.92 


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1.92 


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1.92 


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1.91 


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x.91 


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1.91 


.61 
1.90 


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1.90 


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1.90 


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x.89 


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x.89 


.67 

x.88 


.68 
1.88 


.70 
1.87 


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1.87 




17 


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1.91 


•59 
1.91 


.60 
1.91 


.61 
1.90 


.62 
1.90 


.63 
1.90 


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1.89 


.67 
x.89 


.68 
1.88 


.69 

1.88 


•7X 
1.87 


.72 

1.87 


•74 
1.86 


•75 
1.85 




18 


.61 
1.90 


.62 
1.90 


.63 
1.90 


.64 
189 


.65 

1.89 


.67 
1.89 


1.88 


.69 
1.88 


.70 
1.87 


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1.87 


•73 
T.86 


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1.86 


.76 
185 


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1.84 


•79 
1.84 




19 


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1.89 


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1.89 


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1.89 


.67 

1.88 


.69 
1.88 


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1.87 


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1.86 


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1.96 


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1.85 


1.85 


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x.84 


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1.84 


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x.83 


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1.82 




20 


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1.88 


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1.83 


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21 


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1.87 


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1.86 


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1.85 


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1.85 


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22 


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23 


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x.78 


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1-75 




24 


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1.83 


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1.83 


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1.82 


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1.80 


.89 
1.79 


.91 
x.78 


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1-77 


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x.76 


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x.76 


•97 
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x.74 




25 


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1.83 


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1.82 


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1.81 


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1.81 


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1.80 


.88 
1.80 


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1.79 


•91 
1-78 


.92 
1.77 


•94 
1.77 


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1.76 


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x.76 


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x.74 


1. 01 
1-73 


1.02 

1.72 


z 
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26 


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1.81 


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1.81 


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x.73 


1.02 
1.72 


1.04 
1.71 


1.05 
1.70 


z 
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27 


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1.80 


.88 
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1.79 


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178 


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1.78 


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1.76 


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1-75 


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x.74 


1. 00 
x.73 


X.OI 

x.72 


1.03 
X.7I 


1.05 
1.70 


1.06 
x.69 


1.08 
x.68 




28 


.89 
1.79 


.91 
1.78 


.92 
T.78 


93 
1.77 


•95 

1.76 


.96 

175 


.98 
1-75 


.99 
1-74 


1. ox 
x.73 


1.02 
1.72 


1.04 

x.7i 


1.06 
1.70 


1.07 
x.69 


1.09 
x.68 


1. 11 
1.66 




29 


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1.78 


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1.77 


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1-75 


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1.75 


•99 
x.74 


1. 00 
1.73 


1.02 
i % .72 


1.03 
x.7X 


1.05 
1.70 


x.07 
1.69 


X.08 
1.68' 


X.IO 

1.67 


1.12 
x.66 


I.I4 
X.65 




30 


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1.76 


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1.72 


1.03 
1.71 


x.04 
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1.08 
1.69 


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1.68 


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1.66 


I.X3 
x.65 


1.X4 
x.64 


1. 16 
x.63 




31 


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1.75 


1.74 


1. 00 
1.73 


1.01 
1.73 


1.02 
1.72 


1.04 
1.71 


1.05 
1.70 


1.07 
1.69 


x.09 
1.68 


I.IO 

1.67 


1. 12 
1.66 


1.13 
1.65 


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x.63 


1.17 
1.63 


1.19 
1.61 




32 


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1-74 


1.01 
1.73 


1.02 
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1.71 


1.04 
1.71 


1.06 

169 


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1.68 


1.09 
167 


I. II 
x.66 


1.13 
165 


1. 14 
x.64 


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1. 18 
1.62 


1. 19 
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1. 21 

159 




33 


1.02 
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1.24 
x.57 




34 


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1.66 


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1.16 
1.63 


1.17 
x.62 


1.19 
x.61 


1. 21 
x.59 


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x.57 


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35 


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1.69 


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1.67 


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x.28 
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36 


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1.68 


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1.67 


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1.62 


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1.59 


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x.56 


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1.53 


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x.52 




37 


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1.67 


1. 12 
1.66 


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165 


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1.19 
1. 61 


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1.60 


1.22 
1.58 


1.24 
x.57 


1.25 
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1.27 
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1.29 
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x.52 


x.32 
x.50 




38 


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x.66 


1. 14 
1.65 


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1.64 


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1.63 


1.18 
I.61 


1.20 
1.60 


1. 21 
1.59 


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1.26 
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1.50 


x.34 
x.48 




39 


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1.64 


1.16 


1.17 
1.62 


1.19 
1.61 


1.20 
1.60 


1. 21 


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40 


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1.62 


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1.22 
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1.23 
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1.22 
1.58 


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1-59 


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I 


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xes 1 


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y- 







BROWN Sc SHARPE MFG. CO. 



81 



DIAMETER INCREMENT— {Continued) 

DIAMETER INCREMENT-GEAR 







72 


71 


70 


69 


68 


67 


66 


65 


64 


63 


62 


61 


60 


59 


58 


57 




12 


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25 


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x.84 


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.81 
x.83 


.82 
182 


.83 
1.S2 


.84 
x.81 


.86 
1.81 




28 


.72 
1.86 


•73 
1.86 


•74 
1.86 


.75 
1.85 


.76 
1.85 


•77 
1.85 


.78 
1.84 


.79 
1.84 


.80 

1.83 


.81 

1.83 


.82 
1.82 


.83 
1.82 


.85 
1.81 


.86 
1.81 


.87 
I.80 


.88 
1.80 




29 


.75 
x.86 


•76 
x.85 


.77 
x.85 


.78 
1.84 


.78 
1.84 


•79 
1.84 


.80 
x.83 


.82 
1.83 


.83 
1.82 


.84 
x.82 


.85 
x.81 


.86 
1. 81 


.87 
1.80 


.88 
1.80 


.89 
x.79 


•9X 
1.78 




30 


.77 
1.85 


•78 
1.84 


.79 
1.84 


.80 
1.83 


.81 
1.83 


.82 
1.83 


.83 
1.82 


.84 
1.82 


.85 

1.81 


.86 
1.81 


.87 
1.80 


.88 
1.79 


.89 
*-79 


.91 

1.78 


.92 

x.78 


•93 

1-77 




31 


•79 
1.84 


.80 
1.83 


.82 
1-83 


.82 
1.82 


.83 
z.82 


•&4 
1.82 


.85 
1.81 


.86 

1.81 


.87 
x.8o 


.88 
x-79 


.89 
1-79 


•9X 

x.78 


.92 
x.78 


•93 
*-77 


•94 
x.76 


96 
x.76 




32 


.81 
1.83 


.82 
1.82 


.83 
1.82 


.84 
1.81 


.85 
1.81 


.86 

1.80 


.87 
1.80 


.88 
1.79 


.89 
1.79 


.91 
1.78 


.92 
1.78 


•93 
1.77 


•94 
x.76 


•95 
».7S 


•97 
1.75 


.98 
1.74 




33 


.83 
1.82 


.84 
1. 81 


.85 
1.81 


.86 
180 


.87 
1.80 


.88 
1-79 


.89 
1.79 


.91 
1.78 


.92 

x.78 


•93 
1.77 


•94 
x-77 


•95 
x.76 


96 

x-75 


1.75 


•99 
I.74 


1.00 
x-73 




34 


•85 
1.81 


.86 
1.80 


.87 
1.80 


.88 
1.79 


.89 
1-79 


.91 
1.78 


.92 
1.78 


•93 
1.77 


•94 
x-77 


•95 
x.76 


96 

x -75 


•97 
x-75 


•99 
1.74 


1. 00 
W3 


I.OI 

x-73 


1.02 
1.72 




35 


.87 
1.80 


.88 
1.79 


.89 
1.79 


.90 
1.78 


•92 
1.78 


•93 
1.77 


.94 
1.77 


95 
1.76 


.96 
1-75 


•97 
x-75 


.98 
1.74 


1. 00 
1-73 


1. 01 
X-73 


1.02 

1.72 


1.03 
1.71 


1.05 
1.70 




36 


.89 
1.79 


.90 
1.78 


.91 
1.78 


•93 
1-77 


•94 
l ' 7 l 


•95 
1.76 


.96 
1.76 


.97 
1.75 


.98 
1-74 


•99 
1.74 


1. 00 
1-73 


1.02 

1.72 


1.03 
1.71 


X.04 
1.71 


1.05 

1.70 


1.07 
1.69 




37 


•9« 
1.78 


.92 
1.77 


.93 
1.77 


•95 
1.76 


.96 


.97 
1-75 


.98 

1-74 


•99 
1-74 


1 .00 
1.73 


1. 01 
1.72 


1.03 

1.72 


x.04 
x-7x 


1.05 
x.70 


1.06 
1.69 


1.08 
1.69 


1.09 
1.68 




38 


•93 
x.77 


•94 
1.76 


.95 
1.76 


•97 
1.75 


.98 
X.75 


•99 
1.74 


1. 00 
1.73 


1.01 
x.73 


1.02 
1.72 


1.03 
x.71 


x.05 

1.71 


1.06 
1.70 


1.07 
x.69 


1.08 
1.68 


1. 10 
X.67 


1. 11 
1.66 




39 


95 
1.76 


.96 
1.75 


•97 
1.75 


.98 
1.74 


.99 
X.73 


1. 01 
1-73 


1.02 
1.72 


1.03 
1.71 


X.04 
1.71 


1.05 
1.70 


1.06 
1.69 


x.08 
1.68 


X.09 
1.68 


x.io 
1.67 


x.12 
1.66 


x.13 
x.65 




40 


.97 
1.75 


•97 
1.75 


•99 
i.74 


1.00 
1.73 


1. 01 
1.72 


1.03 
1.72 


1.04 
1.71 


1.05 
1.70 


1.06 
1.70 


1.07 
x.69 


1.08 
1.68 


1. 10 
1.67 


1. 11 
1.66 


1. 12 
1.66 


1. 14 
x.65 


x.15 
x.64 




41 


•99 
1.74 


1. 00 
1.73 


1.01 
1-73 


I.02 
1.72 


103 
x.71 


1.04 
1.71 


1.06 

1.70 


1.07 
1.69 


1.08 
1.68 


1.09 
x.68 


1. 10 
1.67 


1. 12 
1.66 


1.13 
x.6 5 


x.14 
1.64 


x.15 
x.63 


x.17 
1.62 




42 


1. 01 
1.73 


1.02 
1.72 


1.03 
1.72 


1.04 
1.71 


1.05 
1.70 


1.06 
1.69 


1.07 
1.60 


1.09 
x.68 


1. 10 
1.67 


1. 11 
1.66 


1. 12 
1.66 


1.13 

»4i 


1.15 
l.6f 


1.16 
1.4 


X.17 
X.62 


1.19 
x.61 










?or 


Deve 


)\ ge 


ars ^ 


with 


axe 


s at 


righ 


t an 


gles 


onl) 


r. 







Tables for Angle of Edge and Angle 
of Face of Gears 



84 BROWN & SHARPE MFG. CO. 



TABLES FOR ANGLES OF EDGE AND ANGLES 

OF FACE. 

The following four tables have been computed for the 
convenience in calculating data for bevel gears with axes at 
right angle. They do not hold good for bevel gears with axes 
at any other angle. 

To use the tables the number of teeth in gear and pinion 
must be known. 

Having located the number of teeth in the gear on the 
horizontal line of figures at the top of the table, and the num- 
ber of teeth in the pinion on the vertical line of figures on the 
left-hand side, we follow the two columns to the square formed 
by their intersections. 

The two angles found in the same square are the respective 
angles for gear and pinion. The tables are so arranged that 
the angle belonging to the gear is always placed above the 
angle for the pinion. 

The cutting angle for a gear or pinion is equal to the 
angle of face of its mate as given in the following tables. 



BROWN & SHARPE MFG. CO. 



85 



TABLE I. 

ANGLE OF EDGE-GEAR 







41 40 


39 


38 


37 


36 


35 


34 


33 


32 


31 


30 


29 


23 


27 




12 




fft& 

1642' 


7*54' 
176' 


73" 2S 

17 ^2 » 


72-a* 
I7'5S' 


7 '34' 
1S26* 


71 5 ' 

18-55' 


7^34/ 
19 26' 


7- i 
19 59' 


69 '26' 
2034 


6850 

JI40' 


fifths 

21 1|»' 


&731' 

23 29 


6648' 

33 12' 


66 2' 
23 5»' 




13 


7**5 

17" 55 


7*59 r 
iSt' 


7^34' 


71 7' 

iw l '53 J 


7039' 


709' 
t9"5*' 


^9 37 
aq-23' 


&9-5" 
2C55 r 


6a 30' 

21 30 


6753" 

227 ' 


^7iy 
aa 45' 


66 M ; 

a^. 26' 


65 51' 
249' 


656 

a4 54' 


6417' 

35 43' 




14 


71 g' 

i*' jr 


7^43' 
19I7' 


70 15 
19 45 


69'4fr 
20 I4 r 


39 16' 
» a 44' 


6rt r 4S J 
2115* 


6^ 13" 

5 i" 


&7 n 37 J 

22'23 J 


67 □ ■ 
330' 


6623' 
23 37' 


6542^ 
2418' 


^4 59' 
25 -1' 


64 M' 

25^46 


6326' 
3b 34' 


6236' 
2734' 




15 


6954 
Mflfi' 


69-36' 
3034' 


6t>'5« H 

21°2 F 


6S2S* 

2I C 3 J ' 


67*56' 

2i L 4' 


67 23 ' 

2237' 


iS6 # 4fi 

23 12' 


6612 


6533' 
24 27' 


«-4 53 

25 y 


64 10' 

25-50 f 


03 2& r 
a6 34' 


6239* 

27 21' 


6i49 r 


&Q 57"' 

29'3 r 




IS 




68*12' 
2148 ' 


67 "43 ' 

22^8' 


67 it* 

23*50' 


66'37 r 
23-23' 


6b V 

23 : '5^ r 


05 26 

24 34 


644V 

35 12 J 


64 *' 
J5 5*' 


63 26' 

26.JV 


62 42 F 


ja 4' 




60 15' 


59 21' 

3*3^ 




17 


^J ^29' 

22^ I ' 


66*58' 
23* J ' 


66 r 27 r 
33 r 33 r 


65 ; 54 J 
*4 C *' 


65 ^9' 


64"43' 
2517' 


64 <j' 

aj 34' 


6326' 
26 34' 


62^5' 
3715' 


62 1' 

J7 59' 


6115 

a^45' 


60 2S 

a9 3J J 


59 37 r 
3" 23' 




57 48 f 
33 'la' 




18 
IS 


66 1$ 
23^' 


65-46 ' 
24-14' 


65" M' 

V'4&' 


^4 39' 
25 r ai' 


644' 
*55* 


63 & 
a6 3^' 


6a 47' 
27 '3' 


62 6' 
27 54 


61 J3 
a^37' 


6u 38' 
39 22' 


5951 
30 9 r 


59 a r 


53^0' 
3i'5o' 


57 '"!&' 
33 44' 


5619' 
31 '41' 




65^' 
24*52' 


64*36' 
3^24 ' 


643' 

as^' 


63-26* 

26 r 34' 


&2-4IJ 

3711' 


62 to' 
2750* 


61 30' 
2A30 


6048 

29 12 P 


604' 
2956' 


59 *B' 

3042' 


5*3"' 
31 3P 


57 39' 

3a ar 


5& :"' 
33M' 


55 31' 
34^' 


54 52' 

.va' 




2D 


64 -a' 
260' 


6326' 
2634' 




6" 3- 14' 
*7 &' 


61 37 
28 23' 


^57' 
^9'3 r 


6015 
a9 45 


59 32 

3aaS' 


Sfl-47' 
31 13' 


5S*)' 

32-G ' 


57 10' 

3a>' 


56 19' 

33 : 4l^ 


5524' 

34 r 36' 


54"afi' 
35^3' 


53 28' 




21 




6j-t«' 

274 2 ' 


,01 42' 

2* I*t' 


6r4' 

2*56/ 


60 25 

a9 : 35 ■ 


59*5^ 


59 a' 
30*58' 


5* 18' 

31 42 


57 33' 


S6 >3' 

3317' 


W33' 
347 r 


56"' 
35^' 


545' 
35 L, 55' 


537' 


5 a.S' 
37 53' 
5»49'i 
39" | 




22 


61 \l l 
2S 13- 


6iut' 

aS "49' 


6^34' 
3926' 


fry 

.y. :■ 


59 ; *5' 
3*'45' 


5^34' 
3-a6' 


57 5^ 
329 


57 ft' 
5* r 54 f 


5* i9 r 

33 1 ! ' 


5529' 

313" 


M3« T 
35 " 


53 45' 

3^45' 


53 49' 
37 "' 


5150' 
3^1"' 




23 


6042' 


006' 


59 &' 
3032' 


53'49' 
3i u ir 


55*' 
31 5= J 


57 25 r 
3**35' 


5*4^ 
33 19" 


55 5^' 
34 5' 


55 7' 
34 53 


54 ^' 
35*42' 


5326' 
3634' 


5>3i v 

37'a9' 


5^35' 
38 25 


5036 
39 34' 


49 34^ 

4c : 26' 




24 


59 39 
30 21' 


59^' 

3^ 5 V 


5823' 
3i B 37* 


57M4 f 
3*16 


5:- - 
32'5 S ' 


5619' 

5r4'' 


55 33 ' 

34a7 r 


54 47' 
3513 


53 5*' 

36 a- 1 


5i' J ~' 
3^5a r 


52 15* 

37 "45' 


51 20' 

3^4^, 


5033 
39 37' 


4924" 
4036' 


|3 U 
413^' 


o 


25 


5^-J^ 
31 22 


5b V 

32 ' 


57 J »' 
3/40' 


5*4^' 


55 57 J 
34 V 


5$ tj 

34^47' 


54 »' 
35 3^' 


53 40' 
36 20 


5a5" J 

37 9 ' 


520' 

3H0' 


Si 7 ' 
385J' 


50 13' 


49' J M r 
40-46' 


4*14' 
4146 


47 12' 

424^' 


26 


57-37' 
3*23' 


56 5*' 
33 2' 


5fii9' 

33 '41' 


55' 3: r 
34 23 


M*54' 

3.S'6' 


54^io' 
35 50 J 


53 a4' 

^j6_ 


5a 3& 
37 =4' 


5*4*' 
5&V 


5054 
39^ r 


jot' 


495' 
4f 55 f 


4»"7 ' 
41 53' 


47 V 
43 53' 


465 

43 55 


^ 


27 


5638' 
33*22; 


55 59 

34'' 


55'* 
344 *' 


54 3^ 
35^4' 


53-53'l 
3&7 J 


5±r 
_i*i3_: 


San 

37 39' 


5133' 

^3 ■; 


5«43 h 
39 17' 


495* r 

4° 9' 


4V57' 
4«V 


4^0* 
420 ' 


47-3 ' 
4*V 


4TV 
43 5S' 


45 




28 


55 4" 

34 '»^ 


55-0' 


54 r <9' 
3541' 


53"37' 
36 23' 


52 53' 
37 7' 


5^ 

37 52' 


51 20' 


50 3^' 

39 J 2S' 


40 19' 


4§ r 49' 
41 11 


47 55' 
425 


43 =' 


460' 
44 ■■•■ 


45 G 






29 


54 W r 5V3' 

3tf**1 35' 57' 


53"' 

36 3S' 


3-- 19' 
37 - r i 


5^55' 
^5' 


51-9' 
3*51' 


5.J Jl ■ 

39 39 J 


4^3^' 

4^-2.3' 


4841' 
41 19' 


47'4\>' 
420' 


4^54' 

43' 6'' 


45*56' 

11 2 ' 


45 s 








30 


53 4^ 

_a_fr 13 | 


53 = 7' 
36"53' 


52 26' 

37 34' 


5r 42' 

3^1 S' 


50' 5S' 
39~ 2 ' 


50 12' 


49 a4 J 
4036' 


4^35' 

4" 25 


47 43 
4a l 7 J 


46 51 
13 9' 


45 *SF 

44 4" 


45 c 








31 


5? is* 


3/ 47' 


5i 3L r 


504S' 
39" "■ 


39"5S H 


4044' 


<B 2S J 
413a' 


47^39' 
42 21' 


4*47 f 
43*3' 


4554' 
44' V 


45 c 








32 


s«r 

37 5*' 


51' acr 
3#V 


30*38' 
39 '«' 


49"34' 
40 fl' 


499-' 
4^'3i J 


4d'2a r 
4E'3^ J 


4734^ 

42^20 r 


46 44' 
43^' 


43S3' 

44'"7 H 


45' 








33 


51 -iu 


5GJ9' 
39 3*' 


49 4*' 
40-14' 


49 ,J ' 
40*58' 


,0-i6' 
r i 1 ■' 


47 T =9 r 
4?'' 3*' 


4 J ' 41 
43 r 9' 


4551' 

44 y 


45 -' 








34 




49 3^', 
4V23 


4*55' 
415' 


4T 49' 


47" a 5' 
4235 r 


463b' 
4322' 


455»J' 
44 10' 


45 : 








35 


49^1' 

4^29' 


41*12* 


4^55' 


4721 ' 
4? 39' 


46 35' 
43 '5' 


45 4^' 
44 '"la' 


45 








36 


4*43' 


4**0' 
4J r 'o ' 


47**7' 
42*43- 


4f>33' 
43*27' 


45- ;7* 

■14 1 J 


45 : 








37 


47 56 
42V 


47 14' 
4246' 


43 '3°' 


45M6' 
4414' 


45 








38 


44*50' 43 , 33' 


4.T45' 

44^5' 


45 1 








39 


46 26' 


44^7' 


45' 








40 


45 4*' 
44'**' 


45 








41 


45' 







86 



BROWN & SHARPE MFG. CO. 



TABLE I (Continued). 

ANGLE OF EDGE-GEAR 







26 


25 


24 


23 


22 


21 


20 


19 


18 


17 


16 | 15 


14 


13 


12 




12 


24^46 'J aS°3S' 


afe'j4' 


62-^7' 

-7 33' 


61 ij' 

-i l 3?' 


60 '15' 

*?*4? 


3P' 5 S' 


57 44' 
32^ 6' 


5^V 
33 c 4i' 


54"V 


537' 
36 53' 




49 ; ^' 47 *7 
40*36' 42 c 43' 


45 




13 


2G34' 


6231' 
zf*9' 


r.L i.,- 
aa' J 27 ' 


2Q r 2?' 


59^' 
J" '35' 


58 iV 
31V 


3W 

3 j 2 ' 


35'37* 
34^3' 


35°5S' 


S^' 
37'M 1 


5^54' 
39V 


49 r 5 r 
40 c 55 r 


4/"7' 


45' 






14 


St' 42' 


&/45' 


59 f 45' 
3°**5 ' 


£"40 ' 

3**30 


57 32' 


g6V 
33 4i' 


55^ 


53*37' 


37 52' 




4B J 4S' 

41*12' 


4**5*' 

43'** 


45 








15 




3^' 


fro' 

32^0 J 


33V 


5F43' 
34" *7' 


S4"aA' 
35 l J=' 


53 r 7 ' . 
36 53' 


5 [ L 4 2* 


S<JI2 r 

39*4** 


4*35* 

41 v 


40 51 ' 
435' 


4^ 








16 


3^37' 


5^3' 

3= f 'J7 f 


33V 


5fWi' 
$4*49 f 




5242' 

37°^' 


5i-au' 
38*40' 


4 .< .--4 ■ 


4? si' 
41 = 33' 


46*44' 
43*W 


45' 








17 


P4¥ 

33 n' 


55N7' 

3-f U' 


54 -11' 


53P5»* 






49 '-38' 

40"22' 


4^i' 
4^49' 


4o : 33' 
43"" ' 


45* 






z 
o 


13 


55^ 
34V 


35"45' 


53 r 7' 


5i r 57' 
3*V 


5043' 

3^"i7 J 


49'=4' 
4«W 


4&V 
4*fo' 


46*33' 
43 27' 


45* 






z 

a. 


19 


535*' 

.V, -, f 


5^46' 

37 M 


Jh"22' 


in 34 ' 


49'"' 


47"3a' 

4^ 


46 e aS' 1 
43^' 


45 








20 


5* & ' 


51-20' 


y, U ' 

3*4*' 


4$te" 
4fi J 


47 U J 
42*17' 


46*4' 
43"3&' 


45" 








21 


51V 


4L/2 ' 


48*48* 

4^u* 


47W 
43^4' 


46^20' 
43°40 ' 


45 








22 


4^46' 


4*39' 

41 r '2i/ 


47^' 
4*V 


4616' 


45° 








23 


48^0' 

41*3^' 


47^3' 


4&-13' 
43*47' 


45 








24 


47**7' 
4* '43' 


4^10' 
43*5" r 


45" 








25 


4^7' 
43j3' 


<tf 








26 


45" 




_ - tf* 



a N b 

N b 
tan« b =_ 



(See page 18). 



BROWN & SHARPE MFG. CO. 



«7 



TABLE II. 

ANGLE OF EDGE-GEAR 





72 


71 I 70 


69 ] 68 


67 


66 | 65 


84 


63 


62 


61 


60 


59 


53 


57 


12 


60-33 W25' 

r*r\ 9 V 


:s, if 

'M-'' 


93 J' 


iO' L' 


io'9 F 


7 j .-■' 
itftfl' 


79 : J2 4 


79 ^3 

]q 37-I 


79 13' 

10 471 


79' y 

ia ! 57' 


7» 52' 
1L : '8' 


73-41' 
ii^ig] 


73 '30' 
U30* 


7^ W 78 7 r 
11 41'lit "S3' 


13 


10 14'J io'23'l jo j 31' 


7920' 
10 40' 


10 49' 




79 5* r 

Ti 9' 


7&4i' 
ii : ig J 


7**3I' 
11 29' 


7820' 

IS |C 


7^-9' 
u c '5i' 


77 53' 


77^ J 

12 t^ 


77'34' 

I2 n 26' 




14 


j 1 ' 


I/O' 


78 41' ?S 3 a' 

11 ly'j 11 "28' 


78^32 
11" j>' 


7S ti 
11 49' 


7*v 
n 59 


7751 
12V 


77 40' 
i . :-o' 


77 2S' 
1232' 


77"*/ 
1=43' 


77 5' 
12-5S" 


7 r > 3-' 

■a* 


76 39' 

13*2* f 


76 36' 176 12 1 

13^34' 1 1 3^4 h" 
75 F"! 75 15' 
M D 3°lM'45' 


15 


li 6 46 


7S4' 
11 3*' 


7;-54'J77 4t J 
13 '6' Ji2"i6' 


13 26' 




77 ' ' 


7fo' 


764^ 
13U' 


7636' 
1324' 


76-24' 


76' 11' 

I3' : 49' 


7, sa 
14=2' 


7^44' 
1 4' 16' 


16 




77.W 
1243 d 


77*7' |7* l &7' 


7&43 r 

1315' 


7 6-34 r 

n>6' 




7& r lo' 
*3"5o r 


75^5^' 
143 ' 


75 45' 
14*15' 


75^3^ 

14 3»' 


7643' 
1443' 


754' 
M 3 56' 


74 49,74 35' 1 74 19' 
1^11^15 25'^5 r 4t' 


17 


13*17* 


13' 28' 


76' 21*1 70 "la' 

13 39 "13 "50' 


75'5S'i7S-'t5 r 
14 a' 1 M-14' 


75 33 
1427' 


75 **' 
U39' 


MS* 


74 54' 


74 L 40 r 

1 ,■ 


74*5' 


74\i' 
t5 r 49 r 


16^4' 116 20' 


7524 
1636 


18 


7553' 

14 r 


7 5 If 
M M 


75' 35' 75 23' 
M *$' M 37 


75 : i&l74-5* r 

14 50" 15 2' 


74 45 h 


74 3^' 74 l 7' 
I5°29'j 15 43' 


74\3' 

15 57' 


i6ti r 


7333- 
16 J7j^ 


?3 'A 


73 J 2' 

l6 5S h 


7245' 
1715' 


7229 

1; f.i 


19 


75*3" 
H47' 


75 ' ' 
M'59' 


74 49'j74'36" 
13 11' 15 24' 


74'J3'j74 ,! io' 
15 37'i<5 y So" 


16 4 r 


73'42'j 73^; 
16 i'iS'' t6 32 


73 c l3';7-^' 

16 47 '[ 1/2' 


7 j 42 
17*E8" 


7 ■ j'j 
17 34' 


7 2 9 > 7i l '52 J 

lrs"! ibs' 


7134 
1^36 


20 
21 


7429' 


74"i6' 74 3' [73'5P']Xri7'|73^5* 

I5 , 44'|i5 , '57'l l& io'I 16 23'! 16-42' 


7?9' 
16-31' 


72 : 54 r 

I7 : 6' 


7 -'.'39' 

17 3t' 


72-33' [ 72 7' 

■7 37' ' I7 U 33' 


?! 51' 

1S : 9' 


71 - Vl . 
t8'a6! 


7V 16 70 59' 

1 S -44/1 19V 


7040' 


7345' 
(6 13 


16 2fi" 16 42' 


73'4' 7250' 
i6^_1t 7 io' 


7^36 
1724* 


7221' 
17^39' 


17 C 54 


71-50' 
1^ 10' 


71 34' 

iS' J 36' 


7i c i7' 
i£i r 43 J 


710' 


7043' 


70 *l? 

i %3 6 


706 
'9 '54 
6g v i3' 

2047 


30 34 

ji 6' 
68 2' 


22 


73FP 


7^47 17^3' 
17= 13- [17*37' 


72- 19^ 72^4 ' 

17 V lira* 


71 >j- 
1-, 11 


7»34 r 


1 a "41' 


71 3 J 

la^SB' 


7<i-45 r 
19'45 J 


70 z* 
I9"34' 


70^10' 
I960' 


6952' 

20M' 


69 33' 

30 37/ 


23 


73 "i7 r |7'\T t? 1 49' 


7134I7TI9' 

ia"26 r |i&'4i' 


71 3' 

i& L 57' 


7- 17' 
■9"iy 


70-30- 

&9 44 r 
20 i6 J 


p 14 
^946' 


6^-57' 

3Q3' 


69 38' 

2i.i 31' 


6g 20' 

30 "40' 


69-2 ■ 
w 5* 


31 iS' 


6H3i 
2t 33 


24 


7^34'! 71- 19' -\ yyfift¥kj&& 


70-17' 
1ST43 J 


>959 


69 20' 
2034 


2051/ 


61 5<J' 
M LO 


6^31' 
2 J 29' 


6S ri- 

21' 48' 


67 52' 
33 S r 


67 3l r 

33 29/ 


■; 10 

22> 


25 


70-51' 71^36' ^"'^'l 7" '5' 
19 9' lnf^'lis'JS', 19 55' 


69 49' 


ju'ib' 


6y 15 

2u''45' 


6S57' 

2J l' 


6a--4u' r 68-21' 

21 3o'l 21 39' 


6B'3' 
2157' 


67-43' 

23 r X7' 


67 r 33' 

2 2^ 37' 


67 1 * 664I' 
32 53', 23^1 9' 


66 19 


26 


709' J&955' 6937'' 6921' 
'95 1 ' 20 7' ™ j :. .--■ ,g 


69-4- 
»56' 


6&4S r 
n i2' 


6S> J 

2l'30 H 


6S 12' 
31 4» J 


67 54', 67 34' 

2j-6 r _[33"36^ 


67 iy 

22 15 


66 35' 
»i5- 


66 9 34 ' 


6613' 

23 47' 


6551' 
24^' 


6329 
24 ji 


27 


69 af 69 »a 
aff*3£ 2D"5t»' 


68 54' 68 3^ r | 65 ao' 68=3' 
31 6' .ai'M'i 31 40 r J2t 57' 


67 45' 
2a L 15' 


6726' 

32 34' 


67^3' ]6o"4S T 
2*52 r J33 J i2 h 


66 2^' 


^.7' 

2353' 


65 4^ 

=1 ^ 


6523- 

24 3 V 


652' 
24 53 


04 .-9 

-'"! - 1 


28 


6*45' 
any 


»*°3*' 


6S ta r 67 551 67 37' 

21 4S ?2 ; 5' l22'33 r 


67*19' 

2241 


22 59' 


6642 

23 ra' 


66 33' 

2338' 


66 3 - 63 43' 

23 5 Sr |24 J ^ r 


6521' 
2439' 


^4'5'J 
25 1' 


6437' 
23-23 


64 "14' 
35'46' 


6^50 

2f» S'i 


29 


684' 
if 5*' 


0747' 

22 1 3' 


6730' g^-ii'Im?^' 

32 30'j v£$t\ iyb' 


6636' 
23*24' 


66,7- 

^'43' 


*5 57 J 
24 3' 


65 i7 
2423' 


65-16' 
J4 44 r 


&4 55 
25 5 4 


64"34' 
2526' 


64 12' 

23^ 


6350' 

a6 J io' 


6ya6' 
3& r 34 r 


63 2 

26- 53 


30 


a 3' 37' 


67^6 

••St 1 


604SI66 jo 1 66^12' 

2v u r'i 25-30' 2^48' 


65 52' 

24 a ' 


&53yi&Si4;6453 
24 : 27' 1 34 r 4^' i 25 7' 


6432' 

25-iS' 


6,^0 

25 50' 


6349 

36(1' 


.> ,1 


63 3' r 
86 .']7 
62 [8 
2743' 


6i39' 

37 C 2I' 


6214 
2746 


31 


66-4 2' 

33" 43' 


33 35' 


66-& 1 1 65/4S | 65 39' 

23 54 *4fia*|B4 31 


245^' 


6450' 
35 10 


64-ja'j 64 "9 * 
25 "jo'> 25 5» 


634S' 

26 1 2' 


63 *<> 
3fi .:■ 


633' 

yj 37' 


.2 ia 

27 2U' 


61 53 r 

2S'7 ' 




32 


BV 

23-58' 


65 44' flyae'lfi^?' [641?] GtfiB' 

34 ifi r : 24 34'; 24 51" *5 wliS^* 1 


64^' 
J532' 


6.V47 r 
36=13' 


63^6' 

26-34 


63*4' 
2636' 


^242' 

2 7 "1&' 


62^191 6 156^ 

27"4*'|35V 


6132' 
28 2S' 


6r 7 ' 

2>- 3 V 


6q 4 1 

29-19' 


33 


*$ 

*4 37' 


2456- 35-1 5 r| 23-31' 33 IV 26 13 


63^26^ 
36 : 34 n 


&3.5' 
26 J 55' 


6143' 
37 17' 


62 '21' 

27 J 39' 


6i"-5SJ' 

aS u 3' 


61 33' 61-11' 
28'25;23 £ 49' 


6"J47 r 
39 13' 


60' 31 

ag'39' 


5956 J 
JO 4' 


34 


64 4 J'l 6V*5 r ' kf y i 63 46 63 36" 63 5' 
*5^7'| 25' 35' J5 r 55' 1 26 14 '■ » 34' ' 26 Stf 


62 45 r 

27 '5' 


6a ^.; 
2/37' 


63 r 
2759' 


6138' 

?B"23' 


6riy 

2S45' 


OO 52' 6Q-33' 
i^^fl' Jag '32' 


60-3' 

^^ 57 


59 37' 
3«23 f 


59 n J 

■■■-■49 


35 


645' 


63 4 5' 63 26 1 S3 6 ' 6246 1 62 35 

26 15 26-34 r l26;v)'!^7i4!J7'^5' 


6a 4' 

■7 5^ 


61 42' 

3U'lS' 


61 19 
3841 


6u'57 r 
29"3' 


60 3.5' 
^ 27' 
59^' 
309' 


609' ;3945 r 
29 5i'|3^i5' 


3041' 


=^33 ' 
3'' 7' 


3*33' 


36 


6 3 >6' 

*3f! 


63 7' 63 47 J |ta<*7' 
36 r 53/; a 7 : i3'j 27 33' 


b2'6 r |6l'45' 
J7 54 J ^^5 


6123' 

2M37' 


61 1 ' 

«8 ; ? y 


60' jS' 

2ji 22 


6015 


59^27' 
3*33 


592' 
g si 


53'37 
3i-33' 
K 54 
32 &' 


34' 10' 
31 50' 


57-43' 
33-17' 


37 


37 T2' 

6 2 1 [ 
37 4? 


6iia' 6a BT 1 61*48' 

x Tl^\ ^7 5- 

61 51 " &J j.o (in 3 - 

28V 1 a3-3o J | a» sl- 


61 . J 7' 6i 5' 


60 44' 


6j 21 ■ 

29 r 39' 


59 5-v 
3 d 4 ' 


59^5 
3023' 


59 '■- 

30 : 5^ h 


5346' 
3^'M 


57^' 
3333' 


57 > r 

32''59' 


38 


a9-'i3 r J29-34' 


5o'4' 
295*' 


5^4 » 
30*19' 


59^ 


53 54 
3r6 J 


5a'3^' 
3130' 


5*5' 
3^55' 


57 39' 
32 31' 


57 I3 r 
3^4^ 


3646' 
33*M' 


56 1 9 

33^' 


39 


6t J 33' 
28^7' 


ot ] j 
3B47 


60-53' 


6a jl' 

39 -V 


6ff it>',39-43 r 

99^50' 'jof 12' 


59 *y 

30 c 3y 




^ V J 


53145750 
31 46(32 in' 


57 24' 

32 "36' 


5S L 53 J 

33 2" 


Sfi'ja 


366' 5537 

33 54i 34 23 


40 


6o57' 

?93' 


60 56 
29^24 


6o r 'i5" 
2945' 


59 53 
3° 7' 


y^ 3 2J , 59"io r 
3D .'S'lifl's ' 


5a 47' & H' 


5 s,,- 
32 o r 


3=^3 J 


57 "i " J 
32"5^ r 


5*>44 J 
3316' 


5619' 
3341' 


55 sa 

343' 


S3 T 24' 

34 35" 


54 57 

35 3 


41 


60' 20* 

2940' 


60V 
30V 


Jo'3l' 


59' ■i7" i 3* 55', 53 32' 


5S9' 
315'' 


57-45 57^' 
32 15' 3^3'J 


5657' 
33 1 3' 
sFTi y - 
334«- 


5632 

33 J S r 
55S3 r 

34 7' 


566 J 
33 54' 


55 39* 55 r i2" 
34^21' 34*43' 


54^-M' 
35 r i6' 


54 1* 
35=441 


42 


59*45' 


SflfM'f 59' J' 
3036'! i Q "5T 


SB"-^'; 58- 1 Ei '|5755' 
ji-20" 31-4 3" 3*5' 


573*' 
32 28' 


57^- 
3-52 


5&43 r 
33^7 


sT=7 

34 33' 


35° J 


51 33' 
35 27 


54 y 

35 55' 


5. '7 
3*23 



88 



BROWN & SHARPE MFG. CO. 



TABLE II (Continued). 

ANGLEOF EDGE-GEAR 







55 f 55 


54 S3 


52 


51 


50 49 


48 


47 


46 


45 


44 


43 


42 




12 


| 2 V 


7742' 


12-31' 


n J 45' 


77"o' 
ifo' 


76 J 4^ J 


76 Vj 7*»"M' 
*3 u 3o' " 13V 


75'S* 


75"4i r 
j ray 


75 J 23 
M*37' 


75"4" 


74 D 45 r 

'5 I5 J 


74 45^ 

15-35/ 
/,;, li' 


74 3 
i : - /.. 
724* 
17 ^3' 




13 


7 6 n 5 6 J 
if V 




76 ah' 
13 '3 2' 


7***3' 

*3 U 47 


75^' 

1 4*2' 


Z5V 
14^3' 


75°26' 
M J 34' 


75 ; 8' 
MS*' 




74 ,^ 
15":^' 


74"i 3' 


73 J 53' 
16V 


73^34' 
i6 D afi' 




14 


7; tf ■ 


75 L 43' 

14V' 


75~^' 
M 3* 


75 u "' 


74*56' 
t5"4' 


74 n 39' 
I5 3 3I J 


74*«' 
ii'i*' 


74 a i' 
I5 J 57* 


73 a 44 
I6°i6' 


73"a5 r 


73 a 4 


72 e 43' 
^7^ f 


72°4l' 


7i°53' 
t8V 


71 34' 
rtTaS'. 




15 


7jV 


74'44' 


74 -2y' 
15.31' 




73 a 55' 

rttV 


73*37' 
16^3' 


l6° 4 2' 


17 V 


72 U 3U' 
i;°2t* 


72-^' 
?7V' 


71-36' 
lb-4' 


7t g 34 r 


7J°io' 


7f u 4^ 
19V 


19"39' 




1G 


74 v y 


16V 


73 >' 

X6 30' 


7i u i2' 
16*4^ 


7^54" 
17Y/ 


7J J 35 h 
I7 7 J5' 


72-15' 


7i" J 55' 


?i u 34' 

ia°36' 


7I J J3 J 

js g 4*' 


7" u 4y J 


70"a6 r 
1^-34' 


70 i r 


69"35' 

■ 


2051' 




17 




7/4SK 
17" II' 


7*31' 


if 47' 


71-34' 


71^' 


7l a i3' 


70^2' 


7^3°' 
i^3fl 


.7 I ^7'~ 
i& 3 53' 


^'43' 
■-■-■■;■ 


2o P 43' 


5ff^ 


68«Jff 

2^34' 


67-5H 
a3 3 2 r 




18 




7i B 53' 


7* J 34* 




Jo^54' 


7" : A1' 
iy a 37' 


7oPra r 

1^4^' 


6gV 

2o' J 10' 


69 a ib' 
tO"34* 


fi9 a J' 

au D 57' 


68^' 


68^2' 
Ji°4!=i J 


&7 t, 45 J 
22^15' 


67^7' 

22*43' 


23^1 1' 




19 


yrty 

ia is' 


7*37' 

i.V 


K37- 


71A7* 
19V 


69V 

jo^4' 


*»9 D 34; 

20°J6' 


69 s «2' 

2 .|; r 


5S4ES' 
3J J I3' 


6^5 g 25' 

ai c 35' 

■27=47 

i^37* 


22 a i' 


^7 V 34' 


67'6' 
2454' 


66 X 

23 Jj 4' 


6>"io' 


S5"39 

24^31' 




20 


70' j : ' 


7 m 1' 
19*59' 


6941' 




'■v,7- 


^^35' 
21-25' 


21^' 


67 L 4^ 

3i!"[3 r 


66 V 

23*3' 


6*>*jQ f 

23V 


66 l f 


^33' 

24^7' 


»5°3 # 
24 s 57' 


"Sfsa' 




21 


69W 
20°^' 


69V 

3o°54' 


fi»°45' 


6a V 




*7 & 37* 


67 Q i3' 

22^7' 


66 J 45i" 


66*23' 

23°3B* 


65*155' 

44 V 


05 J 2ft' 

24^32' 




64^29' 

63-26' 
'6"34 J 


63"^' 
27^6 ' 


&3'26 J 

26 \4' 

6 _ 2'-Ji r 
27'V 




22 


iflf 


Wis* 


&7"5>' 

22 J tO' 


" U 33 H 


67 J 4' 


23 °«' 


23"45* 


fe 19' 

34*1 J 1 


6S S <*' 


25*5' 


(j4 m 26" 
J5 U 34 J 


&3' 37' 




23 


67°4i 


67W 


«'55' 


66 a ja' 


66^' 


6j g 44 r 
24 n i6 


24^42' 


6iV 
35 V 


64 U 44'^3 J 53' 


65-26 ^2^' 
46 q 34'; 27^4 ' 


62^24' 
2 7 c j6 J 


6t°5i' 

3»^' 


6i s i6' 
J8 6 42' 




24 




^34* 


66 2' 


24 D 22' 


65 J J4'|64 4!i' 


64 D 23' 
<2f3«' 


63 u 54' 
2& J 6" 


63^' 


47 J 3' 


62°27'[6i a 56' 
2J J 33'|2&°4* 


6l a 3^ 

aa^7 


6o°>i' 


6o°iy 
29°4£' 




25 


b 5 4 3? * 

■ft' 


24V 


&y9' 


tM c 45 H 
3S D I5' 


64"**'' 


26 a ;' 


26 J 34' 


6jV 

2? = 2 r 


62 ,J J :5* 
27 a 3t' 


61^9' 

ab"! ' 


bl^'/'Oo^' 


6o c 24' 
29 a 3* f 


5^' J 50' 


5PV4* 
3&*4fi' 


z 



26 
27 


6 3 t. 


64V 
25 D iS J 


fi4 ft ia' 


&3 u sa* 
26^' 




37 V 


bj 3 3i T 

<7°29' 


6=^3' 
27^57' 


^i"33' 
2li J 27- 




6o g 3i' 


5y ft 5bt' 


59^25' 
3^ n 33 J 


5^V 

3I°T0' 


5S^4' 


s. 


63°5i' 

26% ' 




27 a 


37°26' 


6l"V 
a/54' 




6i R ri' 
3b c '53' 


Gu"ja' 
49*22' 


6o J ? ' 
29*33' 


59 U 35 J 


3^2' 

30V 


sagas' 

3i u 32' 


57 a 53' 
32*7' 


37^6' 
32 D 44 r 


u 


28 


a6 u 34 J 


63'' ' 

26 V 


62*3*' 

27^24' 


^51' 


61^42' 

J8 n i8' 


6r u 
*s a 46' 


6o'45' 

a y r, t5' 


6o L '^a' 

^f45 r 


59^45' 
3o :l ^5 , 


59^3' 
39"*? 1 


51 3 jo' 


StJ^" 

3^53' 


57°32' 
3a Q a3' 


S6V 

33 n 4 ' 


56*19' 
33°4f 




29 






6145' 
38 is' 


6i g i£' 




GO*23' 

^ D 37' 


59 33' 

3o"7 J 


W T i3' 
30°37' 


5^ fl 52' 
3l°a' 


S6^9' 
3t fl 4i' 


57 L 46' 
34"M' 


57^4' 
34 S 4S' 


33°43' 


34°o' 


S5°23' 

34 s 37" 




30 


6^49' 
3S : [l' 




6u"57' 

J9T 


tW3°J9' 


6o q i J 


5v D Ji' 
3u' j jS' 


5^3' 

30V 


3i"aS' 


3#^' 


37^7' 
34 u 33 h 


56 g 53' 
3j"7' 


56^19' 


55"43' 
34°17' 


55°5' 
34"55' 


54* 

35"-32' 




31 


61 j j 


ew u j6' 


60-6' 

29 "34' 


5m u 4i' 
30*19' 


30*** 




JV13' 
31'4*' 


5J L 4^' 
32^9' 


3254' 


56V 

33^4' 


13^' 


55 u 4fi^ 
34*34' 


54 l >' 

i5 «o-' 


54*14' 

aft 8 ' 


53W 

y 4T, 




32 




3u a iz p 


3<^39' 


3^' 


3^j6 h 


5; ft i4 r 
3J^' 


57 "23' 

3^37' 


5652' 
33V 


5^9' 

3 f4t' 


55 g 43' 
34 a i5' 


55 J *i' 
54*W 


54 u 35 r 
35^25' 


ii 5&' 

36*2' 


53*21^ 

^39' 


52V 

37 r.' 




33 


3^3*' 

VW' 
p*tf r 


59*2' 


5^*34' 


5ft J 

3i u 35' 


57 a 3^' 
32 a ^4' 


. - j4' 


5^ L 34' 
i3°2&' 


56 V 

i3 5a H 


55^3^' 
34 "3 J' 


54°<A r 
35"4' 


54 u 2i' 


53°45 


53^' 


53'2y' 

37 e 3i' 


5^ : '5^' 
3ii' J 9' 




34 


5VJ0' 
31*44' 


57*4*; 
3^12 


3*V 




33 D 4t' 


55"47'i 
34^3' 


5315' 
34 45' 


54 V 

35^y' 


54 3 7' 
35°i3' 


53'32 J 

3t>°4&' 


52"54' 


54 c iS' 

37*44' 


5i'4«' 
38°40' 


51 J' 




35 


31V 


57V 


57 'J' 
3^7' 


Ja^7' 


H°57' 


55*3 *' 

34 r *8 r 


55^' 
35°o T 


S4 D -^ 
35 V 


53 Q 54' 


53 c ^' 


52 J 44 J 
37*1*' 


37' , 52' 


5i"3°' 


5Q^' 
39^9' 


5u LJ 

39 3 4S' 




35 


57 !*' 


33 D la' 


sTi5' 

33*4 1' 


5^ vr 


53 u ^' 
34 & 4=' 


S4 B 47* 


54 J i5' 
3345* 


53 -■' 
36 id r 


53^ 
3^52' 


37 u 27" 


5J°57 J 
38 u 3' 


5I c 2U f 


5f^3' 
39 D r7' 


5*V 
3^5^ 


I', -4 ' 




37 




5&V 

33^ 


34^-5' 




S4 C J4 ■ 
35 W 


as D 53 f 


53' J 30' 
3*V 


52-56' 
37"4' 


5* p 2j' 

37"i7' 


5i u 47' 
3» W I3' 


51-ia' 

3i> J 4^' 


^ c 35' 
J9 C 25' 


4§W 
40 fl 4' 


*> 5 7' 


4"' 31 
4i D 25' 




38 
39 


34V 
34V 


55^1' 
34*39' 


35,*' 


a-: ~/ 
35 n 3t' 


53'3P 


3& J 42' 


5- .'.' 
J7 M' 


52^1' 
37 '<*' 


5 t c 3= f 

#■24' 


5i D 3' 5^ J 27' 
3^57' 1 39^33' 


4V a 49' 
4o a u' 


49^11* 
40"49' 


4*°34' 
4* a a»' 


47 32' 

42V 




54 "3:/ 
33 c 4i' 


35 V 


S3 :-j 


53V 
Jo u 53' 


53 B 3ft' 

37 J 34' 


5-- 3' 
37^57 * 


51-29' 
3»3^ 


^54' 
39 b o' 
Via' 

3y"4^' 


5tJ u iy' 
59 V 


4^44 

4tf u ib'' 


49 J 5' 

4t> u 35' 


4^27' 
4i°33' 


« B 4^ 

4*-13' 


47"7 F 

4-'53- 




40 




3&V 


53 D ^' 


37 l, 2' 


52 u j6' 
37^34' 


3^' 


jl'JO' 

3*V 


5t> J 4C' 
3^ u M r 


49*36' 
40 24' 


4B°59 J 


4^2 2 ' 
4*°rf 


47°44' 
42 5, i6' 


47^5' 
44°i5' 


43 1* 




41 


36^12' 


y- a. :; 


53 d 4S' 
37^"' 


37 44' 


5l D 45' 
3^15' 


5l D iF 

3*V 


39*2^' 


3y a 55' 


4^30 r 

4o°30' 


4b°54 J 
4 t B 6' 


4&°i7' 
4i g 43' 


47>' 
4*' 20' 


47^1- 
43 g 59' 


40'"22' 

43 J 3S' 


45-41 

•14 1, 




42 


53°*' 


5-.r- 
37"**' 


53^' 

37 D 5=' 


3^4* 




5»*32' .j/ji 1 
3S C ?S'|4«V 


4»°24' 

|B°ifi' 


43^ 
■1 l c n' 


4/ahy 

4l e 47' 


47 u 3&' 
4 ^ - L 4- 


46^39' 

43 -L' 


46^0' 

4aV 


45 Mo' 
44 J au' 


45" 



BROWN & SHARPE MFG. CO. 



8 9 



TABLE III. 

ANGLE OF FACE-GEAR 







41 


40 | 39 


38 


37 


36 


35 | 34 | 33 


32 31 


30 


29 


28 


27 




12 


13 37', «j'5Ti M'-iS 7 

70 '59' 70"i3"l 70 16 


14 39 J 


^5i J 
69*5 


15^4' 
6^32' 


*5"49'| i6 J i5"| i& 43' 1 i7 r l3' 
Sf59' 6723 «6 45 j 66 5 r 


*7 43 J 
_^S'23' 


t^5' 
64fa$' 


63^53* 


1917' 

f»3'3' 


2t>y 

_^2j9_^ 




13 


M*55 r *ri7 r 
69- 45' f 691 s 


I5 L 39 
6S47' 


16V 

17 34' 
$6 56' 


16 ^5' 
^7 J 43 r 


Jfi^i' 
67^9 r 


i7 , i9Jn'-4^' ; iS-i6'li r i4^ T 
W33'|65s6l65 a iS' 64 E 34 




'9 57 r 

63 5' 


2032- 
6/14' 


61*33' 


=^54' 

So''' j * 




14 


ring 

6SV 


i6l4 r 
68 V 


16 j9' 
67 39' 




lfi fl I7 ' 

^547' 


^9" 


T 9 " 16 ' ,' '9'4^": 20 Ja' 


jo '56 

6 1^30 


2134 
fii'33' 


33"t3' 

60^41' 


23*55' 

59^4 7' 


23^' 




15 


1728' 


17 53 
6A'45 J 


18 1 a - 

■v,i j 




653' 


194*' 
64^26' 


20 11' 
6349' 


Jo J 44 r 
63 ; 3 h 


6234: 


21 53 
6t 3j^ 


22 31 " 
6051' 


6o"2' 


2?sr 
599' 


24'35 r 


25 30' 

... 1 1 
271' 

55^43' 




16 
IT 


j3 42 ' 
&5V 


199' 


19 35 

64 5/ 

J" i J 
°J J5 


20-3' 
6423" 


2032' 
6346* 


31 3 P 
637' 


21 3^ ' 

62 2S' 


22 9 ' 

fa 45 


22-45' 


33^32' 

60' 14' 


34 i J 
5/25 J 


24 4^ 
53 34' 


25 'j6' 
574^' 


26': r 
56^4^' 




19^' 

*T54' 


2d J4' 


31-31' 
63V 


2153 
6231 


21 24 
61 50' 


- r -57- 
6i 3 9' 


^3 33 
hi I? 


34 fJ id' 
594o" 


34*50/ 
5SV 


2531 


2&14' 

57^0 


37*59' 
56 13 


27 47' 
5i tS J 


3S^37 H 

54-iJ- 




1S 


5i J £' 
6545' 


« J 37 r 
639' 


336 
G* a 34' 


22 j3' 

Si' 1 56' 


*3 9' 
6rr 7 ' 


33 43' 
So 7 35 r 


34 iS 

59 r 5 2 ' 


34 "5^ 
59 * ' 


^34 ] 
5820' 


26^15' 
57 = 3i' 


5^39' 


27 ] 4=' 


as- 29' 
54*49'' 


a^iS' 
53 50' 


3-V 
52°47 J 




19 
20 


63 3 6 r 
^ -■' 
6130' 


"49 
62 V 


01 at' 


2352' 

6o ] 44 r 


24 -a&' 
60V 


25"i' 
5921 f 


25"37 ' 
5*37' 


26-15' 2fi 5'> r 
j7"51 j l57 j 4' 


5*V[4'! 55^2' 


2'/'3 J 15 5'V 

54'rf'i 53 f 2S h 


JQ 13 
52'2S r 


31-40- 
5^24' 




24 r 
6053' 


*l"3* p 
60 14' 


356' 
5T34' 


=5 -tu 
5^54 r 


S6i6' 
5? 10' 


26°55' 

5735' 


=7'34* 


3h"'i5 j 
35' 49' 


3^-53' 
54 J 5S' 
30^7' 

5343' 


29-44' 
54 r 
31 4 J 
52°S»' 


30-31 *; 31 j 2i* 

53 9 ' ' 53°9' 


33 J t3' 
51 J 9 ^ 


33^' 
5U'4' 




21 


24-39J 25^10' 
to 35'i59 J 4&' 


3543* 
59 7' 


2618' 

5S 2&' 


2*53* 2713d' 
57 -33' %;*' 


z8lo' 
50 M' 


2«'Sd' 


*j ■■-' 
5436 


3152' 

5* &* J 


3^43' 
5o 3 53' 


33^6' 


34"3^" 
4^47' 




22 


25 4&' 
59 '■»' 


Zfr'IQ' 

5SV 


_ ^'5T" 


2727' 

57 i9' 


S&35' 


3 ii43' 
55 5t r 


ag-"23 ' 

55 "4' 


5-1 1: 


30 %*' 


3 1 3T T 
5332' 


32 J2 ' 


33 U 1 

5'-' J 1 


343' 
49*4 *' 


34^57 ' 

4^7' 


35"54 
47 n 33' 




23 


26=52' 


27 ^6' 
$7& 


HS"o' 

5656' 


3a^6 r 

56 "U" 


29^4' 

55>' 


29 33' 
54 13' 




53^ ' 




33 & 3&' 

SP 1 '^' 


34 7 27" 
49 '39' 


43^' 


3^15' 
47°?7 J 


371 2 ' 

46 2o J 




24 


37*57' 

5715" 


2631' 1 a? 7' 
56 35 55 r 53' 

55'34'|54 5*' 


2943' 
55 "' 


30"22' 

54^' 


3 , j- 

53>' 


Jt 9 45' 
5251' 


3^ 'atf' 33'14 H 

52^'i5t^o- 


34 J l' 
50" J 5' 


34 J 50 J 
49'ao' 


Pas "42 r 

4M-3 j ' 


3*35' 
47^21' 


37^' 

46 u iS' 


33*iS' 


z 


25 
26 


■ 56 *5' 
5515' 


3049' 

54'9' 


J-' -v 
53**3' 


32 J io' 
52> f 


3152' 
51 -(^ 


33 f, 3T 
5° J 57" 


34"-'J r 

j° 7 5' 


3511 
49*11' 


3d"o' 
4^14' 


3«52 f 

47 r i f> ' 


37"47 ' 
4 & J 5' 


3S43 h 
45'u' 


3941": 

44 Q 5' 




z 


3033 
54M J 


31 14 

53V 


3^ 5-r 

53"3' 


3^34' 

St"**' 


3315' 

5 f 35' 


33*58' 
5o j j6' 


31 t5 
4^55' 


35 31' 
49 a 3' 


3&"r> h 

43'7 J 


17-10' 
4712' 


3*'2' 

_4_a J t2' 


33 L 56' 
45">o' 


39"53' 
44^7' 


40^52' 
43*2' 


a. 


27 

28 


3*3' 

54 : *9' 


3i*39 r 
53 37' 


law 
5254 


J257' 
52 9' 


3337 r 
51*23' 


34 ''20 r 

5o c 34' 


35 J 3' 
49°45' 


3 ; j 49' 


4& n 2 r 


37 J 25' 
47T 


& 16- 
46 u :o' 


39^1 o 1 
45 J ^ h 


404 ' 
44 io J 


4 s 1 *!' 
43'5' 


42 Q 




3 J a' 
53^2' 


32 39' 
52 -39' 


33 i> 
51 56 


33 57' 
5' n J 


34 39' 
50 ?5 ' 


35^ i" 
49 V 


4^47'i47 5*S' 


37 40 

47 • 


3& J 2g r 
46 7 ' 


39 -2f 

45 n n' 


4d^5j4" ; 9' 
44 ir, 43^9' 


43'7' 






29 
30 




33'3S J 
5* '44' 


34 r 7' 
5" I' 

35 15 

50 7" 


3-J^ 
5P i5" 


3539' 
49-29' 


3^'^3'|37^' 
4S"4i''47 J 50' 


37 54 


3^ i-' 
4& u 4' 


3932 J 
45 u t&' 


40 L 34' 
44 L i2 h 


41 IS 

4 J M" 


1 

4=*I3' 








3357 r 
53 33' 


34 36' 
50'50' 


35 56' 

49-20' 


48 34 


37^1 ' 
47 45" 


3fl^' 
4^55' 


^'53 3V 13' ^3-! 
4S'3' M5V 44^4' 


4i 2 S T 

43 = i7' 


4213' 








31 


35 5.V 
50 ! r ' 


35-3i ' 
49 57' 


it II 
49^3 J 


3^3' 
48*28' 


37 '35' 
47 ] 39 r 


jS J 2d - 

4^2' 


1* (' 


39-52 'j ^41^ 
45-10' 4_p 5 ' 


■U *2 
43 h 20 H 


ta -,. 








32 


35 J*' 
49>' 


36*7' 
497' 


37 *' 
48*23' 


37 4S' 
47 3^ 


4^49'' 45^59 ' 


45 S' 
4056' 
44 J iS' 


4° "49" 

44 17' 


41^' 
43"24 T 


42 ll' 








33 


36 '39' 
4^59' 


37 </ 
43T7 J 


33 O' 
47^2' 


46 ft' 


39"26' 
45^53' 


4d L o' 


4' ;;' 

43'26' 


42 33' 








34 


4^13' 


13"- ir 
47^7' 


1^53' 

46 43' 


J9 35 r i 
4557' 


40 iS 
+5 ''&' 


4^4' 
4420' 


fP.49' 
43 T 29' 


■]= 37' 








35 


3823' 
47^4' 


39 3' 
4639 r 


39'44 r 
45 54 J 


40*26' 
453' 


4l*lo' 

u -■■• 


4155 
43 J 3i ' 


42"4l" 








36 


39" r 
4657 


39S2 J 
45 V 


40 W 

45 & 


41 I5 r 
M a 1 


43 1 T0 r 

43 : 34' 


42 45 








37 


40V 
45V 


4Q J 40 J 
4SB' 


4! |2' 
44 u 2^ h 


425' 

43 c 37' 


42 V 








38 


40^7' 
45 7' 


4i J zS J 
44" 24" 


42V 
4^39" 


42V 








39 


44 24' 


SS«' 








40 


42 lS' 

43 42' 


4*5«' 








41 


A?*' 







go 



BROWN & SHARPE MFG. CO. 



TABLE III (Continued). 
ANGLE OF FACE-GEAR 







26 25 24 23 22 21 20 19 ! 18 


17 16 


15 


14 


13 


12 




12 


6ri4' 6015' 




243' 

5&4y' 


25-2' i 26-j' 
55 3*^54*7' 


j; 11' 
52 39' 


^ *y 


49t7 r 


47=5' 


32 L 44 J 

45 --I 


34*»' 
13 U' 


36 16' 
40°5o' 


#17' 




13 


22-37' 


23 26' 




25 * r 
56 u r 


26 6' 

3^ 5'-' 


278' • 28 14* 
53 J 3 6'|52"J H 


5" 39' 


3042' 

49°=' 


32V 
47'6' 


33*34/ 
45"' 


3&& 


3^55" 
4JlV 


#¥' 






14 


24^5' 
57*49' 


25*16' 


20 8' 


27 5 J 

54^5' 


28 V 
53'* ' 


5147' 


30 JO" 

50 *j' 


31-33' 

-^ 17 


32*52' 
4?*' 


14IS' 

l* 1 <' 

36 ;j' 
45*33' 


35 5*' 
43'^' 

37 _"' 
4l'39* 


4^24' 

39 L 3S' 


39"^' 








15 


26^1' 


ny 
557' 


*7"5*' 


28 58' 

52 44' 


51 26' 


3«' 

502' 


4*33' 


53 ■**•' 

4r^ J 


3456' 
4j 20' 






:s 


275*' 
543*' 


** -15' 
533'' 


*S43' 

52 21 ' 


3^44' 
516' 


3^50' 
49 46' 


48' 22' 


34 1=' 
4052* 


3531' 
4519' 


36" J 54' 


3*>3' 

4 i >r 


39 5/ 








17 


29J« 

53*' 


30 26' 
5*6 


31-26* 
50 4B' 


33 58' 
493*' 


48'ir 


34~47* 
4* "47' 


360' 
45i6 J 


i7 2I 

4 j 43 


^ ■;.-:.■ 
42 '1' 


4" 15' 






7L 




18 


3* -i' 


3** > 


33 J 4' 
49 IB' 


34*8' 
4tfV 


4641' 


3628' 
4516' 


3745' 
43^*5' 


3^5' 
4211'' 


40 31' 






z 


19 




33' J 3*' 
43 V 


34' jS 
47 54 


35 4y' 3^ % 5j" 


3ttfl5' 

43 Sa ' 


42 Ju' 


4«45' 






20 


34*3' 

4^57' 


3*6' 
47 4^ ' 


3W 


37'i6' 


43 ; 52' 


3yJ9' 
4 j ty 


40V 








21 


35"3i' 
47 3/ 


46W 


37 37' 
45 ^' 


33V 


4234 : 4 








22 


3^3*' 
46^4' 


37'" 55' 
45 M' 


3/b ' 

43 L "5S' 


40 S' 
4*V 


4i c io' 








23 


yTi*' 


39"I5' 
*4 c i' 


40 20' 
42*46' 


41 -s' 








24 


3SW 

44 3 ' 


4°''3* J 
42*52' 


4*V 








25 


4<M3' 
42 4 57' 


fli'+fi* 








26 


41 "53 ' 







g.= 90°— (a + fi) 
gb=.90° — (« + /?) 



BROWN & SHARPE MFG. CO. 



91 



TABLE IV. 

ANGLE OF FACE-GEAR 



62 \ 61 



72 71 



70 69 I 68 67 



€6 I 65 64 



60 



59 ! 58 57 



12 



7^ S£ 



13 



b 4 j 

j$i 2 















14 



15 



9 -i<-' 

"i?ll' l{J r 2l J 



9*34' 

77°i6 f 



77 V J 77 V 



94 * 
774' 



;6 4 o- 



18 



1059" 

75' n 55' 



7j6"g 

75*43' 



LQ 'JO' 

7^i a* 



ml 



17 



18 



11 4 J u"5V 

E 1 - : I L - " I 1 In 



12'4 

74^ 



ij"j9f 12 40' 
7 1 ^5' 74 \£ 



74 :t 



19 






73'M' 



20 



tj 57' M l''' 

7^ a7J 7**43' 



21 

22 



73**31 7' "59 ' 



1 4 --'J' 
7*V 



ij u S r 
7iV 



15 37 

7i u J9' 



7114' 



23 



16-12' »6^V 
70° j6'| 7p> ' 



J 3 3J 

7_u L '59 



i6 fi 55'f l ?V 

7'-'.> ; V47' 
*7 39' *7V 
_6g fa r | 69 *4 





66V 



29 



JO -Jr 7 



30 



21-9 



31 



21 U S0' 



32 
33 



22'jl 
64^35: 



2^10' 



34 



*3 5* 



35 



2425' 
62*39' 



36 



&2 L, r 



37 



38 



^5 47 

6^23' 

*)J5 J 
60V 




JS 1 V _V-. 



42 






20-43' 

66*17 ' 



'I **'J9' 



aw 
65 sf 



at 1 



21 43 1 



22*24 
64^6' 



22 .jV 

64^6' 



2J r 3iJ' 



34' : V 

62^ 



24346' 
62° rb' 



25° *7' 
61 V 



26 L 6' 
61V 



36V 
6o a 26 



27°22 

J? C 4S' 



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2y'l2 



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1120 

7_5 U */ 



74"33' 






if 4*' 
23 



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72 V 



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76^ 

7^44' 



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66*22' 



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64^1 



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64 D t7' 



63 V 



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62°i7j 



24 4 



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60 L 4i' 



374 
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3**57' 



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?7*&\ 77*47' 



77 ^ 



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77*' 



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75*55' 
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27 4 
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55 '.W 



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2b D 29 J 

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57°7' 



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55 & '3' 



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17-31' i7 a 4*. 



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67 ^7 ' 



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61 Vj 

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57 D 2j h 



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27"7 

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62-3; ■ 



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56^16 



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53°37 J 



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55"4&' 



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54*3*' 



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58 p aa1 57*34' 



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5739 

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33^2' t 34^9 



66 



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21^50 



22*41 

62 r 49' 



24 ■'-'! 

62 ! 1 



26^46 

59 D 4» 



57 q 37' 
2950 

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33 u i' 
54*39 



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53^ 
33 a H' 

34*^ 

34 r 4t' 

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02 



BROWN & SHARPE MFG. CO. 



TABLE IV (Continued). 

ANGLE OF FACE-GEAR 




Table for Selecting Cutters for 
Bevel Gears 



94 



BROWN & SHARPE MFG. CO. 



CUTTERS FOR USE IN CUTTING BEVEL GEARS. 

PINION. 





12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


28 


29 


30 


12 


7-7 






































13 


6-7 


6-6 




































14 


5-7 


6-6 


6-6 


































13 


5-7 


5-6 


5-6 


5-5 
































16 


4-7 


5-7 


5-6 


5-6 


5-5 






























17 


4-7 


4-7 


4-6 


5-6 


5-5 


5-5 




























18 


4-7 


4-7 


4-6 


4-6 


4-5 


4-5 


5-5 


























19 


3-7 


4-7 


4-6 


4 6 


4-6 


4-5 


4-5 


4-4 
























20 


3-7 


3-7 


4-6 


4-6 


4-6 


4-5 


4-5 


4-4 


4-4 






















21 


3-8 


3-7 


3-7 


3-6 


4-6 


4-5 


4-5 


4-5 


4-4 


4-4 




















22 


3-8 


3-7 


3-7 


3-6 


3-6 


3-5 


4-5 


4-5 


4-4 


4-4 


4-4 


















23 


3-8 


3-7 


3-7 


3-6 


3-6 


3-5 


3-5 


3-5 


3-4 


4-4 


4-4 


4-4 
















24 

25 


3-8 


3-7 


3-7 


3-6 


3-6 


3-6 


3-5 


3-5 


3-4 


3-4 


3-4 


4-4 


4-4 














2-8 


2-7 


3-7 


3-6 


3-6 


3-6 


3-5 


3-5 


3-5 


3-4 


3-4 


3-4 


4-4 


3-3 












26 
27 


2-8 


2-7 


3-7 


3-6 


3-6 


,3-6 


3-5 


3-5 


3-5 


3-4 


3-4 


3-4 


3-4 


3-3 


3-3 










2-8 


2-7 


2-7 


2-6 


3-6 


3-6 


3-5 


3-5 


3-5 


3-4 


3-4 


3-4 


3-4 


3-4 


3-3 


3-3 








28 


2-8 


2-7 


2-7 


2-6 


2-6 


3-6 


3-5 


3-5 


3-5 


3-4 


3-4 


3-4 


3-4 


3-4 


3-3 


3-3 


3-3 






29 


2-8 


2-7 


2-7 


2-7 


2-6 


2-6 


3-5 


3-5 


3-5 


3-4 


3-4 


3-4 


3-4 


3-4 


3-3 


3-3 


3-3 


3-3 




30 


2-8 


2-7 


2-7 


2-7 


2-6 


2-6 


2-5 


2-5 


3-5 


3-5 


3-4 


3-4 


3-4 


3-4 


3-4 


3-3 


3-3 


3-3 


3-3 


31 


2-8 


2-7 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


3-4 


3-4 


3-4 


3-4 


3-4 


3-3 


3-3 


3-3 


3-3 


32 


2-8 


2-7 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-4 


2-4 


3-4 


3-4 


3-4 


3-3 


3-3 


3-3 


3-3 


33 


2-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


3-4 


3-4 


3-4 


3-3 


3-3 


3-3 


34 


2-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


3-4 


3-3 


3-3 


3-3 


35 


2-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


3-3 


3-3 


36 


2-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


2-3 


37 


2-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


2-3 


38 


2-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


39 


2-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


40 


i-8 


2-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


41 


1-8 


i-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


42 


1-8 


i-8 


2-7 


2-7 


2-6 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


2-3 


43 


1-8 


i-8 


1-7 


2-7 


2-6 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


44 


i-8 


i-8 


1-7 


i-7 


2-6 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


45 


1-8 


i-8 


1-7 


i-7 


1 -6 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


46 


i-8 


i-8 


i-7 


i-7 


i-7 


2-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 
2-3 


47 


1-8 


i-8 


1-7 


i-7 


i-7 


1-6 


2-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


48 


i-8 


i-8 


1-7 


i-7 


i-7 


1-6 


1-6 


2-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


49 


i-8 


i-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


50 


i-8 


i-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


2-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-3 


51 


i-8 


i-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


i-5 


2-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


52 


1-8 


i-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


i-5 


i-5 


2-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


53 


i-8 


1-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


2-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


54 


1-8 


1-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 


55 


i-8 


i-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


i-4 


2-4 


2-4 


2-4 


2-4 


2-4 


2-4 



BROWN & SHARPE MFG. CO. 

CUTTERS FOR USE IN CUTTING BEVEL 

(Continued.) 
PINION. 



95 



GEARS. 





12 


13 


14 


15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


28 


29 


30 


56 


1-8 


1-8 


i-7 


i-7 


i-6 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


2-4 


2-4 


2-4 


2-4 


2-4 


57 


1-8 


1-8 


1-7 


1-7 


1-6 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


i-4 


1-4 


1-4 


2-4 


2-4 


2-4 


2-4 


58 


1-8 


1-8 


i-7 


i-7 


1-6 


i-6 


1-6 


i-6 


i-5 


1-5 


i-5 


i-5 


i-4 


1-4 


It4 


1-4 


2-4 


2-4 


2-4 


59 


1-8 


1-8 


1-7 


1-7 


i-6 


i-6 


1-6 


i-6 


i-5 


i-5 


i-5 


i-5 


i-5 


1-4 


i-4 


i-4 


i-4 


2-4 


2-4 


60 


i-8 


1-8 


1-7 


1-7 


1-6 


i-6 


1-6 


i-6 


i-5 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


i-4 


i-4 


i-4 


2-4 


61 


i-8 


1-8 


1-7 


1-7 


1-6 


i-6 


i-6 


i-6 


i-5 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


i-4 


i-4 


i-4 


i-4 


62 


1-8 


1-8 


1-7 


1-7 


i-6 


1-6 


1-6 


i-6 


i-5 


i-5 


i-5 


1-5 


i-5 


1-4 


1-4 


1-4 


i-4 


i-4 


i-4 


63 


i-8 


i-8 


1-7 


1-7 


i-6 


1-6 


1-6 


1-6 


1-5 


1-5 


i-5 


i-5 


i-5 


1-4 


1-4 


i-4 


1-4 


i-4 


1-4 


64 


1-8 


1-8 


1-7 


i-7 


1-6 


i-6 


1-6 


i-6 


1-6 


i-5 


1-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


i-4 


i-4 


65 


1-8 


1-8 


i-7 


1-7 


1-7 


1-6 


i-6 


1-6 


i-6 


1-5 


i-5 


i-5 


i-5 


1-4 


1-4 


i-4 


i-4 


i-4 


i-4 


66 


1-8 


1-8 


1-7 


i-7 


i-7 


1-6 


i-6 


1-6 


1-6 


i-5 


i-5 


i-5 


1-5 


1-4 


1-4 


i-4 


1-4 


i-4 


i-4 


67 


1-8 


1-8 


1-7 


1-7 


i-7 


1-6 


1-6 


1-6 


1-6 


i-5 


1-5 


i-5 


1-5 


1-4 


i-4 


i-4 


'i-4 


i-4 


i-4 


68 


1-8 


1-8 


1-7 


i-7 


1-7 


1-6 


i-6 


1-6 


i-6 


i-5 


i-5 


i-5 


1-5 


1-4 


1-4 


i-4 


i-4 


i-4 


i-4 


69 


1-8 


1-8 


1-7 


i-7 


i-7 


1-6 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


1-4 


i-4 


i-4 


1-4 


i-4 


1-4 


70 


1-8 


1-8 


1-7 


1-7 


i-7 


1-6 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


i-4 


1-4 


71 


1-8 


1-8 


i-7 


i-7 


i-7 


1-6 


1-6 


1-6 


i-6 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


1-4 


1-4 


72 


1-8 


i-8 


1-7 


1-7 


i-7 


1-6 


1-6 


1-6 


1-6 


1-5 


i-5 


i-5 


1-5 


1-4 


i-4 


1-4 


1-4 


i-4 


1-4 


73 


i-8 


1-8 


i-7 


1-7 


i-7 


1-6 


i-6 


1-6 


1-6 


i-5 


i-5 


i-5 


1-5 


1-4 


i-4 


1-4 


1-4 


1-4 


1-4 


74 


i-8 


1-8 


1-7 


1-7 


i-7 


1-6 


1-6 


1-6 


1-6 


1-5 


1-5 


i-5 


1-5 


i-4 


1-4 


i-4 


1-4 


1-4 


1-4 


75 


1-8 


1-8 


i-7 


1-7 


i-7 


1-6 


i-6 


1-6 


1-6 


i-5 


1-5 


1-5 


i-5 


i-4 


i-4 


i-4 


1-4 


1-4 


1-4 


76- 


1-8 


1^8 


1-7 


1-7 


i-7 


1-6 


1-6 


1-6 


1-6 


1-5 


i-5 


i-5 


1-5 


i-4 


1-4 


1-4 


1-4 


i-4 


1-4. 


77 


1-8 


1-8 


i-7 


1-7 


1-7 


1-6 


i-6 


1-6 


1-6 


i-5 


i-5 


i-5 


r-5 


i-4 


i-4 


1-4 


1-4 


1-4 


1-4 


78 


i-'s 


1-8 


i-7 


i-7 


1-7 


1-6 


i-6 


1-6 


1-6 


1-5 


1-5 


i-5 


1-5 


1-4 


1-4 


1-4 


i-4 


i-4 


1-4 


79 


i-8 


1-8 


i 7 


i-7 


i-7 


1-6 


i-6 


1-6 


1-6 


1-5 


1-5 


1-5 


1-5 


1-4 


1-4 


1-4 


1-4 


i-4 


1-4 


80 


1-8 


1-8 


i-7 


1-7 


1-7 


1-6 


i-6 


1-6 


1-6 


1-5 


i-5 


i-5 


i-5 


1-4 


1-4 


1-4 


i-4 


1-4 


1-4 


81 


1-8 


1-8 


i-7 


1-7 


1-7 


1-6 


i-6 


i-6 


1-6 


1-5 


1-5 


i-5 


i-5 


1-4 


i-4 


1-4 


1-4 


i-4 


1-4 


82 


1-8 


1-8 


i-7 


1-7 


1-7 


1-6 


1-6 


i-6 


i-6 


i-5 


1-5 


i-5 


i-5 


1-4 


i-4 


1-4 


i-4 


i-4 


1-4 


83 


1-8 


i-8 


1-7 


1-7 


i-7 


1-6 


i-6 


1-6 


1-6 


1-5 


i-5 


1-5 


i-5 


1-4 


1-4 


1-4 


1-4 


1-4 


1-4 


84 


1-8 


i~8 


1-7 


1-7 


1-7 


1-6 


1-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


1-4 


1-4 


85 


1-8 


1-8 


i-7 


1-7 


1-7 


1-6 


i-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


i-4 


1-4 


1-4 


1-4 


i-4 


1-4 


86 


1-8 


1-8 


i-7 


1-7 


1-7 


1-6 


i-6 


1-6 


1-6 


i-5 


1-5 


i-5 


i-5 


1-4 


1-4 


1-4 


i-4 


i-4 


1-4 


87 


1-8 


i-8 


i-7 


i-7 


i-7 


1-6 


i-6 


i 6 


1-6 


1-5 


i-5 


1-5 


i-5 


1-4 


1-4 


1-4 


1-4 


1-4 


i-4 


88 


1-8 


1-8 


1-7 


1-7 


i-7 


1-6 


i-6 


1-6 


1-6 


i-5 


1-5 


i-5 


i-5 


i-4 


i-4 


1-4 


i-4 


1-4 


1-4 


89 


1-8 


i-8 


i-7 


1-7 


1-7 


1-6 


1-6 


i-6 


1-6 


1-5 


i-5 


i-5 


1-5 


1-4 


i-4 


1-4 


1-4 


1-4 


1-4 


90 


1-8 


i-8 


1-7 


1*7 


1-7 


1-6 


i-6 


1-6 


i-6 


i-5 


i-5 


i-5 


i-5 


1-4 


i-4 


1-4 


1-4 


i-4 


i-4 


91 


1-8 


i-8 


i-7 


1-7 


1-7 


1-6 


i-6 


1-6 


1-6 


1-5 


1-5 


i-5 


i-5 


1-4 


1-4 


i-4 


1-4 


i-4 


1-4 


92 


i-8 


1-8 


1-7 


1-7 


1-7 


i-6 


i-6 


1-6 


1-6 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


1-4 


1-4 


93 


i-8 


1-8 


i-7 


i-7 


1-7 


1-6 


i-6 


1-6 


1-6 


1-5 


i-5 


i-5 


1-5 


1-4 


1-4 


1-4 


i-4 


1-4 


1-4 


94 


i-8 


1-8 


i-7 


i-7 


1-7 


i-6 


i-6 


1-6 


1-6 


i-5 


i-5 


i-5 


1-5 


1-4 


1-4 


i-4 


1-4 


i-4 


1-4 


95 


1-8 


i-8 


i-7 


1-7 


1-7 


i-6 


i-6 


1-6 


i-6 


i-5 


i-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


i-4 


1-4 


96 


1-8 


1-8 


1-7 


1-7 


1-7 


i-6 


i-6 


1-6 


1-6 


i-5 


1-5 


1-5 


1-5 


1-4 


1-4 


1-4 


i-4 


1-4 


1-4 


97 


i-8 


i-8 


i-7 


1*7 


i-7 


i-6 


1-6 


1-6 


i-6 


1-5 


1-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


i-4 


1-4 


98 


i-8 


i-8 


1-7 


i-7 


1-7 


i-6 


1-6 


1-6 


1-6 


i-5 


1-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


1-4 


1-4 


99 


i-8 


1-8 


1-7 


1-7 


i-7 


i-6 


1-6 


i-6 


1-6 


1-5 


1-5 


i-5 


i-5 


1-4 


1-4 


i-4 


1-4 


1-4 


1-4 


100 


i-8 


1-8 


i-7 


1*7 


i-7 


i-6 


1-6 


1-6 


1-6 


1-5 


1-5 


i-5 


i-5 


1-4 


1-4 


1-4 


1-4 


1-4 


1-4 






Natural Sines and Cosines 
Natural Tangents and Cotangents 



9» 



BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES 



/ 








I 





2 





3 





4° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 





.00000 




.01745 


.99985 


.03490 


.99939 


.05234 


.99863 


.06976 


.99756 


60 


X 


.00029 






.01774 


.99984 


.03519 


.99938 


.05263 


.99861 


.07005 


.99754 


59 


2 


.00058 
.00087 






.01803 


.99984 


.03548 


.99937 


.05292 


.99860 


.07034 


.99752 


58 


3 






.01832 


.99983 


.03577 


4)9936 


.05321 


.99858 


.07063 


•99750 


57 


4 


.00116 






.01862 


.99983 


.03606 


.99935 


.05350 


.99857 


.07092 


.99748 


56 


5 


.00145 






.01891 


.99982 


.03635 


•99934 


.05379 


.99855 


.07121 


.99746 


55 


6 


.00175 






.01920 


.99982 


.03664 


.99933 


.05408 


.99854 


.07150 


•99744 


54 


7 


.00204 






.01949 


•V998i 


.03693 


.99932 


.05437 


.99852 


.07179 


•99742 


53 


8 


.00233 






.01978 


.9998o 


.03723 


.99931 


.05466 


.99851 


.07208 


.99740 


52 


9 


.00262 






.02007 


.99980 


.03752 


•99930 


.05495 


.99849 


.07237 


.99738 


51 


10 


.00291 






.02036 


•99979 


.03781 


.99929 


.05524 


.99847 


.07266 


.99736 


50 


ii 


.00320 


.99999 


.02065 


.99979 


.03810 


.99927 


•05553 


.99846 


.07295 


•99734 


49 


12 


.00349 


.99099 


.02094 


.99978 


.03839 


.99926 


.05582 


.99844 


.07324 


•99731 


48 


13 


.00378 


.99999 


.02123 


.99977 


.03808 


.99925 


.05611 


.99842 


•07353 


.99729 


47 


14 


.00407 


.99999 


.02152 


•99977 


.03897 


.99924 


.05640 


.99841 


.07382 


.99727 


46 


IS 


.00436 


.99999 


.02181 


.99976 


.03926 


.99923 


.05669 


.59839 


.07411 


.99725 


45 


16 


.00465 


•99999 


.02211 


.99976 


.03955 


.99922 


.05698 


.59838 


.07440 


.99723 


44 


17 


.00495 


.99999 


.02240 


.99975 


.03984 


.99921 


.05727 


.99836 


.07469 


.99721 


43 


18 


.00524 


.99999 


.02269 


.99974 


.04013 


.99919 


.05756 


.99834 


.07498 


.99719 


42 


19 


.00553 


.99998 


.02298 


.99974 


.04042 


.99918 


.05785 


.99833 


.07527 


.99716 


41 


20 


.00582 


.99998 


.02327 


.99973 


.04071 


.99917 


.05814 


.99831 


.07556 


.99714 


40 


21 


.00611 


.99998 


.02356 


.99972 


.04100 


.99916 


.05844 


.99829 


.07585 


.99712 


39 


22 


.00640 


.99998 


.02385 


.99972 


.04129 


.99915 


.05873 


•59827 


.07614 


.99710 


38 


*3 


.00669 


•c:998 


.02414 


•99971 


.04159 


.99913 


.05902 


.99826 


.07643 


.99708 


37 


24 


.00698 


.99998 


.02443 


.99970 


.04188 


.99912 


.05931 


.99824 


.07672 


.99705 


36 


2S 


.00727 


.99997 


.02472 


.99969 


.04217 


•999II 


.05960 


.99822 


.07701 


.99703 


35 


26 


.00756 


.99997 


.02501 


.99969 


.04246 


.99910 


.05989 


.99821 


.07730 


.99701 


34 


27 


.00785 


.99997 


.02530 


.99968 


.04275 


.99909 


.06018 


.99819 


.07759 


.99699 


33 


28 


.00814 


.99997 


.02560 


.99967 


.04304 


.99907 


.06047 


.99817 


.07788 


.99696 


32 


29 


.00844 


.99996 


.02589 


.99966 


.04333 


.99906 


.06076 


.99815 


.07817 


.99694 


31 


30 


.00873 


.99996 


.02618 


.99966 


.04362 


.99905 


.06105 


.09813 


.07846 


.99692 


30 


31 


.00902 


.99996 


.02647 


.99965 


.04391 


.99904 


.06134 


.09812 


.0787s 


99689 


29 


32 


.00931 


.90996 


.02676 


.99964 


.04420 


.99902 


.06163 


.99810 


.07904 


,99687 


28 


33 


.00960 


•99995 


.02705 


.99963 


.04449 


.90901 


.06192 


.99808 


.07933 


99tt] 


27 


34 


.00089 


.99995 


.02734 


.99963 


.04478 


.99900 


.06221 


.99806 


.07962 


,9VfiS3 


26 


35 


.01018 


•99995 


.02763 


.99962 


.04507 


.99893 


.06250 


.99804 


.07991 


.wt-*o 


25 


36 


.01047 


.99995 


.02792 


.99961 


.04536 


.99897 


.06279 


.99803 


.08020 


90678 


24 


37 


.01076 


.99594 


.02821 


.99960 


.04565 


.99396 


.06308 


.99801 


.08049 


.99676 


23 


38 


.01105 


.99994 


.02850 


•99959 


.04594 


.99894 


.06337 


•99799 


.08078 


^59*?3 


22 


39 


.01134 


.99994 


.02879 


•99959 


.04623 


.99893 


.06366 


.99797 


.08107 


.99671 


21 


40 


.01164 


•99993 


.02908 


.99958 


.04653 


.99892 


.06395 


•99795 


.08136 


.99668 


20 


41 


.01193 


•99993 


.02938 


•99957 


.04682 


.09890 


.06424 


•99793 


.08165 


.99666 


19 


42 


.01222 


•99993 


.02967 


.99956 


.047" 


.99889 


.06453 


.99792 


.08194 


.99664 


l8 


43 


.01251 


•99992 


.02996 


.99955 


.04740 


.99888 


.06482 


.99790 


.08223 


.99661 


17 


44 


.01280 


.99992 


.03025 


•99954 


.04769 


.99886 


.06511 


.99788 


.08252 


.99659 


16 


45 


.01309 


.99991 


.03054 
.03083 


•99953 


.04798 


.99885 


.06540 


.99786 


.08281 


.99657 


15 


46 


.01338 


.99991 


.99952 


.04827 


.99883 


.06569 


.99784 


.08310 


.99654 


14 


47 


.01367 


•99991 


.03112 


•99952 


.04856 


,99382 


.06598 


.99782 


.08339 


.99652 


13 


48 


.01396 


.99990 


.03141 


.99951 


.04885 


.99881 


.06627 


.99780 


.08368 


.99649 


12 


49 


.01425 


•99990 


.03170 


.99950 


.04914 


.99879 


.0C656 


.99778 


.08397 


.99647 


II 


SO 


.01454 


.99989 


.03199 


•99949 


.04943 


.99878 


.06685 


.99776 


.08426 


.99644 


10 


Si 


.01483 


.99989 


.03228 


.99948 


.04972 


.99876 


.06714 


.99774 


.08455 


.99642 


9 


52 


.01513 


.99989 


.03257 


.99947 


.05001 


.99875 


.06743 


•99772 


.08484 


.99639 


8 


53 


.01542 


.99988 


.03286 


.99946 


.05030 


.99873 


.06773 


•99770 


.08513 


.99637 


7 


54 


.01571 


.99988 


.03316 


.99945 


.05059 


.99872 


.06802 


.99768 


.08542 


.99635 


6 


55 


.01600 


.99987 


.03345 


•99944 


.05088 


.99870 


.06831 


.99766 


.08571 


.99632 


5 


56 


.01629 
.01658 


.99987 


.03374 


•99943 


.05117 


.99869 


.06S60 


.99764 


.08600 


.99630 


4 


57 


.99986 


.03403 


•99942 


.05146 


.99867 


.06889 


.99762 


.08629 


.99627 


3 


58 


.01687 


.99986 


.03432 


.99941 


.05175 


.99866 


.06918 


.99760 


.08658 


.99625 


2 


59 


.01716 


.99985 


.03461 


.99940 


.05205 


.99864 


.06947 


.99758 


.08687 


.99622 


I 


60 


.01745 


.99985 


.03490 


.99939 


.05234 


.99863 


.06976 


.99756 


.08716 


.99619 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


& 


)° 


Si 


1° 


8; 


7° 


8( 


5° 


8 


5° 



BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES 



99 



/ 


5 





6 


O 


7 





8 





9° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine C 


Cosine 





.087x6 


.09619 


.10453 


.99452 


.12187 


.09255 


.13917 


.99027 


.15643 


.98769 


60 


X 


.08745 


.09617 


.10482 


.99449 


.12216 


.99251 


.13946 


.99023 


.15673 


98764 


3 


a 


.08774 
.08803 


.99614 


.1051 X 


.99446 


.12245 


.99248 


.13975 


.99019 


.15701 


.98760 


3 


.99612 


.10540 


.99443 


.12274 


.99244 


.14004 


.99015 


.15730 


98755 


57 


4 


.08831 


.99609 


.10569 


•99440 


.12302 


.99240 


.14033 


.99011 


.15758 


98751 


56 


5 


.08860 


.99607 


•IOS97 


•99437 


.12331 


.99237 


.14061 


.99006 


•15787 


98746 


55 


6 


.08889 


.99604 


.10626 


•99434 


.12360 


.99233 


.14090 


.99002 


.15816 


98741 


54 


I 


.08918 


.99602 


.10655 


.99431 


.12389 


.99230 


.14119 


.98998 


.15845 


98737 


53 


.08947 


•99599 


.10684 


.99428 


.12418 


.99226 


.14148 


.98994 


.15873 


98732 


52 


9 


.08976 


.99596 


.10713 


.99424 


.12447 


.99222 


.14177 


.98900 


.15902 


98728 


51 


10 


.00005 


.99594 


.10742 


.99421 


.12476 


.99219 


.14205 


.98986 


.15931 


98723 


50 


ii 


.09034 


.99591 


•I077I 


.99418 


.12504 


.99215 


.14234 


.9S982 


.15959 


uSrrt 


49 


12 


.09063 


.99588 


.10800 


•99415 


.12533 


.99211 


.14263 


.93978 


.15988 


■a ~ ■ - 


48 


13 


.00092 


.99586 


.10829 


.99412 


.12562 


.99208 


.14292 


.98973 


.16017 


'.•'T" 1 


47 


14 


.09121 


•99583 


.10858 


.99409 


.12591 


.99-04 


.14320 


.98969 


.16046 


■>;o4 


46 


IS 


.09150 


.99580 


.10887 


.99406 


.12620 


.99200 


.14349 


.98965 


.16074 




45 


16 


.09179 


.99578 


.10916 


•99402 


.12649 


.99197 


.14378 


.98961 


.16103 


9S&95 


44 


17 


.09208 


•99575 


•10945 


.99399 


.12678 


.99193 


.14407 


.93957 


.16132 


i>r.,.,.i 


43 


18 


.09237 


.99572 


.10973 


.99396 


.12706 


.99189 


.14436 


.98953 


.16160 


■ .■*■ f ■'■ 6 


42 


19 


.09266 


.09570 


.11002 


•99393 


•12735 


.99186 


.14464 


.98948 


.16189 


986^1 


41 


20 


.09295 


.99567 


.11031 


•99390 


.12764 


.99182 


.14493 


.98944 


.16218 


Qfc'676 


40 


21 


09324 


.99564 


.11060 


.99386 


.12793 


.99178 


.14522 


.98940 


.16246 


98671 


39 


22 


.09353 


.99562 


.11089 


.99383 


.12822 


.99175 


.14551 


.98936 


.16275 


98667 


38 


23 


.09382 


.99559 


.11118 


.9938o 


.12851 


.99171 


.14580 


.98931 


.16304 


98662 


37 


24 


.09411 


.99556 


.11147 


•99377 


.12880 


.99167 


.14608 


.98927 


.16333 


98657 


36 


25 


.09440 


•99553 


.11176 


•99374 


.12908 


.99163 


.14637 


.9S923 


.16361 


98652 


35 


26 


.09469 


•99551 


.11205 


•99370 


.12937 


.99160 


.14666 


.98919 


.16390 


9S648 


34 


s 


.09498 


•99543 


.11234 


.99367 


.12966 


.99156 


.14695 


.98914 


.16419 


98643 


33 


.09527 


•99545 


.11263 


.99364 


.12995 


.99152 


.14723 


.98910 


.16447 


98638 


32 


29 


.09556 
.09585 


.99542 


.11291 


.99360 


.13024 


.99148 


.14752 


.98906 


.16476 


98633 


31 


30 


•99540 


.11320 


•99357 


.13053 


.99144 


.14781 


.93902 


.16505 


98629 


30 


31 


.00614 


•99537 


.11349 


•99354 


.13081 


.99141 


.14810 


.08897 


.16533 


98624 


29 


32 


.00642 


•99534 


.11378 


•99351 


.13110 


.99137 


.14838 


.98893 


.16562 


98619 


28 


33 


.09671 


•99531 


.11407 


•99347 


.13139 


.99133 


.14867 


.98889 


.16591 


98614 


27 


34 


.09700 


.99528 


.11436 


.99344 


.13168 


.99129 


.14896 


.98884 


.16620 


98609 


26 


35 


.09729 


.99526 


.11465 


•99341 


.13197 


.99125 


.14925 


.9838o 


.16648 


98604 


25 


36 


.09758 


.99523 


."494 


•99337 


.13226 


.99122 


.14954 


.98876 


.16677 


98600 


24 


37 


.09787 


.99520 


.11523 


.99334 


.13254 


.99"8 


.14982 


.98871 


.16706 


98595 


23 


38 


.09816 


.99517 


."552 


.99331 


.13283 


.99114 


.15011 


.98867 


.16734 


98590 


22 


39 


.09845 


.995M 


.11580 


.99327 


.13312 


.99110 


.15040 


.98863 


.16763 


98585 


21 


40 


.09374 


•995 11 


.11609 


.99324 


.13341 


.99106 


.15069 


.98858 


.16792 


98580 


20 


41 


.00903 


.99508 


.11638 


.99320 


.13370 


.99102 


.15097 


.98854 


.16820 


qP ? 75 


19 


42 


.00932 


.995o6 


.11667 


.99317 


.13399 


.99098 


.15126 


.98849 


.16849 


#,;,;, 


18 


43 


.09061 


.99503 


.11696 


.99314 


•13427 


.99094 


.15155 


.98845 


.16878 




17 


44 


.09990 


.99500 


.11725 


.99310 


.13456 


99091 


.15184 


.98841 


.16906 


9&5.6I 


16 


45 


.10019 


.99497 


•II754 


.99307 


.13485 


.99087 


.15212 


.98836 


.16935 


,.':;f, 


IS 


46 


.10048 


•99494 


."783 


.99303 


.13514 


.99083 


.15241 


.98832 


.16964 


f^Ys] 


14 


47 


.1C077 


.99491 


.11812 


.99300 


.13543 


•99079 


.15270 


.98827 


.16992 


■ : ,!. 


13 


48 


.10106 


.99488 


.11840 


.99297 


.13572 


.99075 


.15299 


.98823 


.17021 


9S5JI 


12 


49 


.10135 


.99485 


.11869 


.99293 


.13600 


.99071 


.15327 


.98818 


.17050 


OSjjQ 


II 


50 


.10164 


.99482 


.11898 


.99290 


.13629 


.99067 


.15356 


.98814 


.17078 


9853I 


10 


51 


.10192 


•99479 


.11927 


.99286 


.13658 


.90063 


.15385 


.98809 


.17107 


98526 


9 


53 


.10221 


.99476 


.11956 


.99283 


.13687 


.99059 


.15414 


.98805 


.17136 


98521 


8 


53 


.10250 


•99473 


.11985 


.99279 


.13716 


.09055 


.15442 


.98800 


.17164 


98516 


7 


54 


.10279 


•99470 


.12014 


.99^76 


.13744 


.99051 


.15471 


.98796 


.17193 


985" 


6 


55 


.10308 


.90467 


.12043 


.99272 


.13773 


.99047 


.15500 


.98791 


.17222 


98506 


5 


56 


.10337 


.99464 


.12071 


.99269 


.13802 


.99043 


.15529 


.98787 


.17250 


98501 


4 


5' 


.10366 


.99461 


.12100 


.99265 


.13831 


.99039 


.15557 


.98782 


.17279 


98496 


3 


58 


.10395 


.99458 


.12129 


.99262 


.13860 


.99035 


.15586 


.98778 


.17308 


98491 


2 


59 


.10424 


.99455 


.12158 


.99258 


.13889 


.99031 


.15615 


.98773 


.17336 


98486 


I 


6o 


.10453 


.99452 


.12187 


.99255 


.13917 


.99027 


.15643 


.98769 


.17365 


9848I 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


8. 


\° 


8; 


1° 


8; 


2° 


8] 


i° 


8o< 


> 



IOO BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES 



/ 


10° 


n° 


12° 


13° 


14° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 





.17365 


.98481 


.19081 


.08163 


.20791 


.07815 


22495 


.97437 


.24192 


.97030 


60 


I 


.17393 


.98476 


.19109 


.98157 


.20820 


.97809 


.22523 


.97430 


.24220 


•97023 


59 


a 


.17422 


.98471 


.19138 


.98152 


.20848 


.97803 


.22552 


.97424 


.24249 


.97015 
.07008 


58 


3 


.17451 


.98466 


.19167 


.98146 


.20877 


•97797 


.22580 


.97417 


24277 


57 


4 


.17479 


.98461 


.19195 


.98140 


.20905 


•97791 


.22608 


.97411 


.24305 


.97001 


56 


5 


.17508 


.98455 


.19224 


.98135 


.20933 


.97784 


.22637 


.97404 


.24333 


.96994 


55 


6 


I7S37 


.98450 


.19252 
.19281 


.98129 


.20962 


.97778 


.22665 


.97398 


.24362 


.96987 


54 


7 


.17565 


.98445 


• 9 5 I2 4 


.20990 


97772 


.22693 


•97391 


.24390 


.96980 


53 


8 


.17594 


.98440 


.19309 


.98118 


.21019 


.97766 


,22722 


.97384 


.24418 


•56973 


52 


9 


.17623 


.98435 


.19338 


.98112 


.21047 


.9776o 


.22750 


.97378 


.24446 


.96966 


51 


10 


.17651 


.98430 


.19366 


.98107 


.21076 


•97754 


.22778 


97371 


.24474 


.96959 


50 


ii 


.17680 


.08425 


.19395 


.98101 


.21104 


.97748 


.22807 


.97365 
•97358 


.24503 


.96952 


49 


12 


.17708 


.98420 


.19423 


.98096 


.21132 


•97742 


.22835 


.24531 


.96945 


48 


13 


.17737 


.98414 


.19452 


.98090 


.21161 


•97735 


.22863 


•97351 


.24559 
.24587 


.96937 


47 


14 


.17766 


.98409 


.19481 


.98084 


.21189 


.97729 


.22892 


•97345 


,96930 


46 


15 


.17794 


.98404 


.19509 


.98079 


.21218 


.97723 


.22920 


.97338 


.24615 


.96923 


45 


16 


.17823 


.98399 


•19538 


.98073 


.21246 


.97717 


.22948 


.97331 


.24644 


.S6916 


44 


17 


• i7 Ip 


.98394 


.19566 


.98067 


.21275 


.977" 


.22977 


.97325 


.24672 


.56909 


43 


18 


.17880 


.98389 


.19595 


.98061 


.21303 


.97705 
.97698 


.23005 


.97318 


.24700 


.96902 


42 


19 


.17909 


.98383 


.19623 


.98056 


.21331 


.23033 


.973" 


.24728 


.56894 


41 


20 


.17937 


.98378 


.19652 


.98050 


.21360 


.97692 


.23062 


.97304 


.24756 


.96887 


40 


21 


.17966 


.98373 


.19680 


.98044 


.21388 


.97686 


.23090 


.97298 


.24784 


.96880 


39 


22 


.17995 


.98363 


.19709 


.98039 


.21417 


.97680 


.23118 


.97291 
.97284 


.24813 


.56873 


38 


23 


.18023 


.98362 


.19737 


.98033 


.21445 


.97673 


.23146 


.24841 


.9686a 


37 


24 


.18052 


.98357 


.19766 


.98027 


.21474 


.97667 


.23175 


.97278 


.24869 


.96858 


36 


25 


.18081 


.98352 


.19794 


.98021 


.21502 


.97661 


.23203 


.97271 


.24897 


96#S I 


35 


26 


.18109 


?98347 


.19823 


.98016 


.21530 


•97655 


.23231 


.97264 


.24925 


.06844 


34 


27 


.18138 


.98341 


.19851 


.98010 


.21559 


.97648 


.23260 


•97257 


.24954 


■06637 


33 


28 


.18166 


.98336 


.19880 


.98004 


.21587 


.97642 


.23288 


.97251 


.24982 


.068 i9 


32 


29 


.18195 


.98331 


.19908 


.97998 


.21616 


.97636 


.23316 


.97244 


.25010 


.96S22 


31 


30 


.18224 


.98325 


.19937 


•97992 


.21644 


.97630 


.23345 


.97237 


.25038 


.96815 


30 


3i 


.18252 


.98320 


.19965 


.97987 


.21672 


.97623 


.23373 


.97230 


.25066 


.96807 


29 


32 


.18281 


.98315 


.19994 


.97981 


.21701 


.97617 


.23401 


.97223 


.25094 


.96800 


28 


33 


.18309 


.98310 


.20022 


•97975 


.217-9 


.97611 


.23429 


.97217 


.25122 


.96793 


27 


34 


.18338 


.98304 


.20051 


.97969 


.21758 


.97604 


.23458 


.97210 


.25151 


.96786 


26 


35 


.18367 


.98299 


.20079 


.97963 


.21786 
.21814 


.97598 


.23486 


.97203 


.25179 


.96778 


25 


36 


.18395 


.98294 


.20108 


.97958 


.97592 


.23514 


.97196 


.25207 


.96771 


24 


% 


.18424 


.98288 


.20136 


•97952 


.21843 


.97585 


.23542 


.97189 


.25235 


.96764 


23 


.18452 


.98283 


.20165 


.97946 


.21871 


.97579 


.23571 


.971S2 


.25263 


.96756 


22 


39 


.18481 


.98277 


.20193 


.97940 


.21899 


•97573 


.23599 


.97176 


.25291 


.96749 


2\ 


40 


.18509 


.98272 


.20222 


.97934 


.21928 


.97566 


.23627 


.97169 


.25320 


.96742 


20 


41 


.18538 


.98267 


.20250 


.97928 


.21956 


•97S6o 


.23656 


.97162 


.25348 


.96734 


19 


42 


.18567 


.98261 


.20279 


.97922 


.21985 


•97553 


.23684 


•97155 


.25376 


.96727 


18 


43 


.18595 


.98256 


.20307 


.97916 


.22013 


.97547 


.23712 


.97148 


.25404 


.96719 


17 


44 


.18624 


.98250 


.20336 


.97910 


.22041 


•97541 


.23740 


.97141 


.25432 


.96712 


16 


45 


.18652 


.98245 


.20364 


.97905 


.22070 


•97534 


.23769 


.9/134 


.25460 


.96705 


15 


46 


.18681 


.98240 


.20393 


.97899 


.22098 


•97528 


.23797 


.97127 


.25488 


.96697 


14 


% 


.18710 


.98234 


.20421 


.97893 


.22126 


.97521 


.23825 


JQ7120 


.25516 


.96690 


13 


.18738 


.98229 


.20450 


.97887 


.22155 


.97515 


.23853 


•97II3 


.25545 


.96682 


12 


49 


.18767 


.98223 


.20478 


.97881 


-22183 


.97508 


.23882 


.97106 


•25573 


.96675 


II 


50 


.18795 


.98218 


.20507 


.97875 


.22212 


.97502 


.23910 


.97ioo 


.25601 


.96667 


10 


51 


.18824 


.98212 


.20535 


.97869 


.22240 


.97496 


.23938 


.97093 


.25629 


.96660 


9 


52 


.18852 


.98207 


.20563 


.97863 


.22268 


^)7489 


.23966 


.97086 


.25657 


.96653 


8 


53 


.18881 


.98201 


.20592 


.97857 


.22297 


.97483 


.23995 


.97079 


.25685 


.96645 


7 


54 


.18910 


.98196 


.20620 


.97851 


.22325 


«97476 


.24023 


.97072 


.25713 


.96638 


6 


55 


.18938 


.98190 


.20649 


.97845 


.22353 


.97470 


.24051 


.97065 


.25741 


.96630 


5 


56 


.18967 


.98185 


.20677 


.97839 


.22382 


.97463 


.24079 


.97058 


.25769 


.96623 


4 


57 


.1899s 


.98179 


.20706 


.97833 


.22410 


•97457 


.24108 


.97051 


.25798 


.96615 
.96608 


3 


58 


.19024 


.98174 


-20734 


.97827 


.22438 


.97450 


.24136 


.97044 


.25826 


2 


59 


.10052 


.98168 


.20763 


.97821. 


.22467 


•97444 


.24164 


.97037 


.25854 


.96600 


I 


60 


.19081 


.98163 


.20791 


.97815 


.22495 


.97437 


.24192 


.97030 


.25882 


.96593 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


79° 


78° 


7; 


7° 


7< 


*-o 


7 


5° 



BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES' 



IOI 



/ 


15° 


i6° 


17° 


18 


I 


9° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 





.25882 


.96593 
.96585 


.27564 


.96126 


.39337 


.95630 


.30903 


.95106 


.32557 
.32584 


•94552 


60 


I 


.35910 


.27592 


.96118 


.39265 


.9562a 


.30939 


SB 


•94543 


$ 


a 


.25938 


.96578 


.27620 


.96110 


.29293 


.95613 


.30957 
.30985 


.3261a 


•94533 


3 


.25966 


.96570 


.37648 


.96102 


.39321 


.95605 


.95079 


.32639 


.94533 


57 


4 


.35994 


.96562 


.37676 


.96094 
.96086 


.39348 


.95596 


.31013 


.95070 


.33667 


.945U 


56 


5 


.36022 


.9655s 


.37704 


.39376 


.95588 


.31040 


.95061 


.32694 


.94504 


55 


6 


.26050 


.96547 


.37731 


.96078 


.39404 


•95579 


.31068 


.95052 


.32723 


.94495 
.94485 


54 


I 


.26079 


.96540 


•377S9 


.96070 


.39433 


•95571 


.31095 


.95043 


.32749 


53 


.26107 


.96532 


.37787 


.96062 


.39460 


•9556a 


.31123 


.95033 


.32777 


.94476 


52 


9 


.26135 


.96524 


.37815 


.06054 


.29487 


.95554 


.31151 


.95024 


.32804 


.94466 


51 


io 


.26163 


.96517 


.37843 


.96046 


.29515 


.95545 


.3"78 


.95015 


.3283a 


•94457 


SO 


ii 


.26191 


.96509 


.37871 


.96037 


.39543 


.95536 


.31206 


.95006 


.32859 


.94447 


49 


13 


.26219 


. .96502 


.27899 


.96039 


.29571 


.95538 


.31233 


•94997 


.32887 


.94438 


48 


13 


.26247 


.96494 


.37927 


.96031 


.39599 


.95519 


.31361 


.94988 


.32914 


.94428 


47 


14 


.26275 


.96486 


.27955 
.27983 


.96013 


.39626 


•955" 


.31389 


.94979 


.32942 


.94418 


46 


IS 


.26303 


.96479 


.96005 


.29654 


.95503 


.31316 


.94970 


.32969 


.94409 


45 


16 


.26331 


96471 


.28011 


•95997 


.29682 


.95493 


.31344 


.94961 


.32997 


.94399 


44 


17 


.36359 


.96463 


.28039 


.95989 


.29710 


•95485 


.3137a 


•94952 


.33024 


•94390 


43 


18 


.36387 


.96456 


.28067 


.95981 


.29737 


.95476 


.31399 


.94943 


.33051 


.94380 


42 


19 


.36415 


.96448 


.28095 


•95972 


.29765 


.95467 


.31427 


.94933 


.33079 


.94370 


41 


30 


.36443 


.96440 


.28123 


.95964 


•29793 


.95459 


.3M54 


.94924 


.33106 


.94361 


40 


21 


.36471 


.96433 


.28150 


.95956 


.29821 


•95450 


.3148a 


.94915 


.33134 


.94351 


39 


aa 


.36500 


.96425 


.28178 


.95948 


.29849 


.95441 


.31510 


.94906 


.33161 


.94342 


38 


23 


.36528 


.96417 


.28206 


.95940 


.29876 


.95433 


.31537 


.94897 


.33189 


•94332 


37 


24 


.26556 
.26584 


.96410 


.28234 


.95931 


.29904 


.95424 


.31565 


.94888 


.33216 


.94322 


36 


as 


.96402 


.2836a 


.95923 


.29932 


.95415 


.31593 


.94878 


.33244 


.94313 


35 


26 


.2661a 


.06394 


.28290 


.95915 


.29960 


•95-107 


.31620 


.94869 


.33271 


.94303 


34 


3 


.36640 


.96386 


.28318 


.95907 


.29987 


.95398 


.31648 


.94860 


.33298 


.94293 


33 


.36668 


.06379 


.28346 


.95898 


.30015 


.95389 


•31675 


.94851 


.33326 


.94264 


32 


29 


.36696 


.96371 


.28374 


.95890 


.30043 


.9538o 


.31703 


.94842 


.33353 


.94274 


31 


30 


.26734 


.96363 


.28402 


.95882 


.30071 


•95372 


.31730 


.9483a 


.33381 


.94264 


30 


31 


-3675a 


.96355 


.28429 


.95874 


.30098 


.95363 


.31758 


.94823 


•33408 


.94254 


39 


3» 


.36780 


.06347 


.28457 


.95865 


.30126 


.95354 


.31786 
.31813 


.94814 


.33436 


.94245 


28 


33 


.363o8 


.96340 


.28485 


.95857 


.30154 
.30182 


•95345 


.94805 


.33463 


.94235 


27 


34 


.36836 


.06332 


.28513 


.95849 


05337 


.31841 


.94795 
.94786 


.33490 


.94225 


26 


35 


.36864 


.96324 


,28541 


.95841 


.30209 


.95328 


.31868 


.33518 


.94215 


25 


36 


.36893 


.96316 


.28569 


.95832 


.30237 


.95319 


.3 189 j 


•94777 
.94768 


•33545 


.94206 


34 


% 


.36920 


.96308 


.28597 


.95824 


.30265 


•95310 


.31923 


•33573 


.94196 


*3 


.26948 


.96301 


.28635 


.95816 


.30^92 


•95301 


.31951 


•94753 


.33600 


.94186 


22 


39 


.26976 


.96293 


.28652 
.28680 


.95807 


.30320 


.95293 


.31979 


•94749 


.33627 


.94176 


21 


40 


.27004 


.96285 


.95799 


.30348 


.95284 


.33006 


•94740 


3365s 


.94167 


30 


41 


.27032 


96277 


.28708 


•95791 


.30376 


•9S27S 


.32034 


•94730 


.33682 


.94157 


19 


4a 


.27060 


.96269 


.38736 


.95782 


.30403 


.95266 


.32061 


.94721 


•33710 


.94M7 


18 


43 


.37088 


.96261 


.38764 


,95774 


.30431 


.95257 


.32089 


.94712 


•33737 


.94137 


17 


44 


.27116 


.96253 


428792 


•95766 


.30459 


.95248 


.32116 


•94702 


.33764 


.94127 
.94118 


16 


45 


.37144 


.96246 


-28820 


•95757 


.30486 


.95240 


.32144 


.94693 


.33792 


15 


46 


.37173 


.96238 


.28847 


•95749 


.30514 


.95231 


.32171 


.94684 


.33819 


.94108 


14 


47 


.37200 


.96230 


*8875 


•95740 


.30542 


.95222 


.32199 


.94674 


.33846 


.94098 


13 


48 


.27228 


.96223 


.28903 


•95732 


.30570 


.95213 


.32227 


.94665 


.33874 


.94088 


12 


49 


.27256 
.27284 


.96214 


-28931 


.95724 


.30597 


.95204 


.32254 


.94656 


•33901 


.94078 


II 


SO 


.96206 


.28959 


•957 1 5 


.30625 


.95195 


J2282 


.94646 


.33929 


.94068 


10 


51 


•37312 


.96108 


128987 


.95707 


.30653 
.30680 


.95186 


.32309 


.94637 


.33956 


.94058 


I 


52 


.37340 


.96190 


.29015 


.95698 


.95177 


.32337 


.94627 


.33983 


.94049 


53 


.37368 


.9618a 


.29042 


^5690 
.95681 


.30708 


.95168 


.32364 • 


.94618 


.34011 


.94039 


7 


54 


.27396 


.96174 


.29070 


.30736 


•95159 


.32392 


.94609 


.34038 


.94039 


6 


55 


.37424 


.96166 


.29098 


.95673 


.30763 


.95150 


.32419 


•94599 


.34065 


.94019 


5 


56 


.27452 


.96158 


.29126 


.95664 


.30791 


.95142 


.32447 


.94590 


.34093 


.94009 


4 


S l 


.27480 


.96150 


.29154 


.95656 


.30819 


.95133 


.32474 


.94586 


.34120 


.93999 


3 


58 


.37508 


.96142 


.29182 


.95647 


.30846 


.95124 


.32502 


•94571 


.34147 


.93989 


a 


59 


.37536 


.96134 


.29209 


.95639 


.30874 


.95"5 


.32529 


•94S6i 


•34175 


•93979 


1 


60 


.27564 


.96126 


.29237 


.95630 


.30902 


.95106 


•32557 


.94552 


.34203 


.93969 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


74° 


7: 


$° 


72 


2° 


71 





7< 


3° 



102 BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES 



/ 


20° 


21° 


22° 


23° 


24° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 





.3420a 


.93969 


.35837 


.93358 


• 374 ?J 


.92718 


.39073 


.92050 


.40674 


.91355 


60 


I 


.34229 


•93959 


.35804 


.93348 


.37488 


.92707 


.39100 


.92039 


.40700 


.91343 


3 


2 


.34257 


.93949 


.35891 


.93337 


.37515 


.92697 


.39127 


.92028 


.40727 


.91331 


3 


.34284 


93939 


.35918 


.93327 


•37542 


.92686 


.39153 
.39180 


.92016 


.40753 


.91319 


57 


4 


.343" 


.93929 


•35945 


.93316 


.37569 


.92675 


.92005 


.40780 


.91307 


56 


5 


.34339 


.93919 


.35973 


.93306 


•37595 


.92664 


.39207 


.91994 


.40806 


.91295 


55 


6 


.34366 


.93909 


.36000 


.93295 


.37622 


.92653 


.39234 


.91982 


.40833 


.91283 


54 


I 


.34393 


.93899 


.36027 


.93285 


.37649 


.92642 


.39260 


.91971 


.40860 


.91272 


53 


•34421 


.93889 


.36054 


.93274 


.37676 


.92631 


.39287 


.91959 


.40886 


.91260 


52 


9 


.34448 


.93879 


.36081 


.93264 


.37703 


.92620 


.393M 


.91948 


.40913 


.91248 


51 


10 


•34475 


.93869 


.36108 


.93253 


.37730 


.92609 


•39341 


.91936 


.40939 


.91236 


50 


ii 


•34503 


.93859 


.36135 


.93243 


•37757 


.92598 


.39367 


.91925 


.40066 


.91224 


49 


12 


.34530 


.93849 


.36162 


.93232 


.37784 


.92587 


.39394 


.91914 


.40992 


- .91212 


48 


13 


•34557 


.93839 


.36190 


.93222 


.37811 


.92576 


.39421 


.91902 


.41019 


.91200 


47 


14 


.34584 


.93829 


.36217 


.93211 


.37838 


.92565 


.39448 


.91891 


.41045 


.91188 


46 


15 


.34612 


.93819 


.36244 


93201 


•3786s 


.92554 


.39474 


.91879 


.41072 


.91176 


45 


16 


•34639 


.93809 


36271 


.93190 


.37892 


.92543 


.39501 


.91868 


.41098 


.91164 


44 


17 


.34666 


•93799 


.36208 


.93180 


.37919 


.92532 


.39528 


.91856 


.41125 


91152 


43 


18 


.34604 


.93789 


.36325 


.93169 


.37946 


.92521 


.39555 


.91845 


.41151 


.91140 


42 


19 


.34721 


.93779 


.36352 


.93159 


•37973 


.92510 


.39581 


•91833 


.41178 


.91128 


41 


20 


.34748 


93769 


.36379 


.93148 


.37999 


.92499 


.39608 


.91822 


.41204 


.91116 


40 


21 


•34775 


93759 
.93748 


.36406 


.93137 


.38026 


.92488 


.39635 


.91810 


.41231 


.91104 


3 2 


22 


.34803 


.36434 


.93127 


.38053 
.38080 


.92477 


.39661 


.91799 


.41257 


.91092 


38 


23 


.34830 


93738 


.36461 


.931 16 


.92466 


.39688 


.91787 


.41284 


.91080 


37 


24 


.34857 


93728 


.36488 


.93106 


.38107 


.92455 


.39715 


.91775 


.41310 


.91068 


36 


25 


.34884 


.93718 


.36515 


.93095 


.38134 


.92444 


•39741 


.91764 


.41337 


.91056 


35 


26 


.34912 


.93708 


.36542 


.93084 


.38161 


.92432 


.39768 


.91752 


.41363 


.91044 


34 


27 


.34939 


.93698 


.36569 


.93074 


.38188 


.92421 


•39795 


.91741 


..41390 


.91032 


33 


28 


.34966 


.93688 


.36596 


.93063 


.38215 


.92410 


.39822 


.91729 


.41416 


.91020 


32 


29 


•34993 


.93677 


.36623 


.93052 


.38241 


.92399 


.39848 


.91718 


.41443 


.91008 


31 


30 


.35021 


93667 


.36650 


.93042 


.38268 


.92388 


.39875 


.91706 


.41469 


.90996 


30 


3i 


.35048 


93657 


.36677 


.93031 


.38205 


.92377 


.39902 


.91694 


.41496 


.90984 


29 


32 


.35075 


.93647 


.36704 


.93020 


.38322 


.92366 


.39928 


.91683 


.41522 


.90972 


28 


33 


.35102 


93637 


.36731 


.93010 


.38349 


•92355 


•39955 


.91671 


.41549 


.90960 


27 


34 


.35130 


.93626 


.36758 


.92999 


.3S376 


.92343 


.39982 


.91660 


.41575 


.00948 


26 


35 


.35157 


.93616 


.36785 


.92988 


.38403 


.92332 


.40008 


.91648 


.41602 


.90936 


25 


36 


.35184 


.93606 


.36812 


.92978 


.38430 


.92321 


.40035 


.91636 


.41628 


.90924 


24 


% 


.352" 


.93596 


.36839 


.92967 


.38456 
.38483 


.92310 


.40062 


.91625 


.41655 


.90911 


23 


.35239 


.93585 


.36867 


.92956 


.92299 


.40088 


.91613 


.41681 


.90899 


22 


39 


.35266 


•93575 


.36894 


.92045 


.38510 


.92287 


.40115 


.91601 


.41707 


.90887 


21 


40 


.35293 


93565 


.36921 


.92935 


.38537 


.92276 


.40141 


.91590 


.41734 


.90875 


20 


41 


.35320 


93555 


.36948 


.92924 


.38564 


.92265 


.40168 


.91578 


.41760 


.90863 


19 


42 


•35347 


•93544 


.36975 


.92913 


.38591 


.92254 


.40195 


.91566 


.41787 


.ooSsi 


18 


43 


•35375 


•93534 


.37002 


.92902 


.38617 


.92243 


.40221 


.91555 


.41813 


.90839 


17 


44 


•35402 


.93524 


.37029 


.92892 


.38644 


.92231 


.40248 


.91543 


.41840 


.90826 


16 


45 


.35429 


■935M 


.37056 


.92881 


.38671 


.92220 


.40275 


.91531 


.41866 


.90814 


15 


46 


•35456 


.93503 


.37083 


.92870 


.38698 


.92209 


.40301 


..91519 


.41892 


.90802 


14 


47 


.35484 


•93493 


.37"0 


.92859 


.38725 


.92198 


.40328 


.91508 


.41919 


.90790 


13 


48 


.355" 


.93483 


.37137 


.92849 


.38752 


.92186 


.40355 


.91496 


.41945 


.90778 


12 


49 


•35538 


•93472 


.37164. 


.92838 


.38778 


.92175 


.40381 


.91484 


.41973 


.90766 


11 


50 


.35565 


.93462 


.37191 


.92827 


.38805 


.92164 


.40408 


.91472 


.41998 


.90753 


10 


51 


.35592 


•93452 


.37218 


.92816 


.3883a 


.92152 


.40434 


.91461 


.42024 


.90741 


9 


52 


.35619 


•93441 


.37245 


.92805 


.38859 


.92141 


.40461 


.91449 


.42051 


.00729 


8 


53 


.35647 


•93431 


.37272 


.92794 


.38886 


.92130 


.40488 


.91437 


.42077 


.90717 


7 


54 


.35674 


•93420 


.37299 


.92784 


.38912 


.92119 


.40514 


.91425 


.42104 


.90704 


6 


55 


.35701 


•93410 


.37326 


.92773 


.38939 


.92107 


.40541 


.91414 


.42130 


.90692 


5 


56 


.35728 


•93400 


•37353 


.92762 


.38966 


.92096 


.40567 


.91402 


.42156 


.90680 


4 


57 


•35755 


.93389 


.37380 


.92751 


.38993 


.92085 


.40594 


.91300 


.42183 


.90668 


3 


58 


.35782 


•93379 


.37407 


.92740 


.39020 


92073 


.40621 


.91373 


.42209 


.00655 


2 


59 


.35810 


.93368 


•37434 


.92729 


.39046 


.92062 


.40647 


.91366 


.42235 


.00643 


I 


60 


.35837 


.93358 


.37461 


.92718 


.39073 


.92050 


.40674 


.91355 


.42262 


.90631 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


6c 


)° 


6* 


S° 


6; 


7° 


6( 


3° 


6 


5° 



BROWN & SHARPE MFG. CO. 



io 3 



NATURAL SINES AND COSINES 



/ 


25° 


26° 


27° 


28° 


29° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 





.42262 


.00631 


.43837 


.80879 


.45399 


.89101 


.46947 


.88295 


.48481 


.87462 


60 


I 


.42288 


.90618 


.43863 


.89867 


.45425 


.89087 


.46973 


.88281 


.48506 


.8:448 


% 


a 


.42315 


.90606 


.43889 


•89854 


.45451 


.89074 


.46999 


.88267 


.48532 


•87434 


3 


.42341 


.90594 


.43916 


.89841 


.45477 


.89061 


.47024 


.88254 


.48557 


.87420 


57 


4 


.42367 


.90582 


.43942 


.89828 


•45503 


.89048 


.47050 


.88240 


.48583 


.87406 


56 


f 


•4*394 


.90569 


.43968 


.89816 


.45529 


.89035 


.47076 


.88226 


.48608 


.87391 


55 


6 


.42420 


•90557 


.43994 


.89803 


•45554 


.89021 


.47101 


.88213 


.48634 


•87377 


54 


I 


.42446 


.00545 


.44020 


.89790 


.45580 


.89008 


.47127 


.88199 


.48659 


.87363 


53 


.42473 


.00532 


.44046 


.89777 


.45606 


.88995 


.47153 


.88185 


.48684 


.87349 


52 


9 


.42499 


.00520 


.44072 


.89764 


.45632 


.88981 


.47178 


.88172 


.48710 


.87335 


51 


10 


.43525 


.90507 


.44098 


.89752 


.45658 


.88968 


.47204 


.88158 


.48735 


.87321 


SO 


ii 


•42552 


.00495 


.44124 


.89739 


.45684 


.88955 


.47229 


.88144 


.48761 


-87306 


49 


12 


.42578 


.90483 


.44151 


.89726 


.45710 


.88942 


.47255 


.88130 


.48786 


.87292 


48 


13 


.42604 


.90470 


.44177 


.89713 


.45736 


.88928 


.47281 


.88117 


.48811 


,87i?8 


47 


14 


.42631 


.00458 


.44203 


.89700 


.45762 


.88915 


.47306 


.88103 


.4*837 


.Byj64 


46 


IS 


.42657 


.00446 


.44229 


.89687 


.45787 


.88902 


•47332 


.88089 


.48862 


&72S0 


45 


16 


.42683 


.00433 


.44255 


.89674 


.45813 


.88888 


.47358 


.88075 


.48888 


B7-35 


44 


\l 


.42709 


.90421 


.44281 


.89662 


.45839 


.88875 


.47383 


.88062 


.48913 


.87*21 


43 


.42736 


.90408 


.44307 


.89649 


•45865 


.88862 


.47409 


.88048 


.48938 


■Kr-< 7 


42 


19 


.42762 


.90396 


•44333 


.89636 


.45891 


.88848 


.47434 


.88034 


.48964 


.87193 


41 


20 


.42788 


.90383 


.44359 


.89623 


.45917 


.88835 


.47460 


.88020 


.48989 


.8717* 


40 


21 


.42815 


.00371 


.44385 


.89610 


.45942 


.88822 


.47486 


.88006 


.49014 


.87164 


39 


22 


.42841 


.00358 


•4441 1 


.89597 


.45968 


.88808 


.47511 


.87993 


.45040 


.87150 


38 


*3 


.42867 


.90346 


•44437 


.89584 


•45994 


.88795 


.47537 


.87979 


.45065 


.87156 


37 


24 


.42894 


.90334 


.44464 


.89571 


.460*0 


.88782 


.47562 


.87965 


.49090 


.87121 


36 


^s 


.42920 


.90321 


.44490 


.89558 


.46046 


.88768 


.47588 


.87951 


.49116 


.87107 


35 


26 


.42946 


.00309 


.44516 


.89545 


.46072 


.88755 


.47614 


.87937 


.49141 


.87093 


34 


^ 


.42972 


.90296 


.44542 


.89532 


.46097 


.88741 


.47639 


.87923 


.49166 


.87079 


33 


.42999 


.90284 


.44568 


.89519 


.46123 


.88728 


.47665 


.87509 


.49192 


.87064 


32 


29 


.43025 


.90271 


.44594 


.89506 


.46149 


.88715 


.47690 


.87856 


.49217 


.87050 


31 


30 


.43051 


.00259 


.44620 


.89493 


.46175 


.88701 


.47716 


.87882 


.49242 


.87036 


30 


31 


•43077 


.90246 


.44646 


.89480 


.46201 


.88688 


.47741 


.87868 


.49268 


.87021 


29 


32 


.43104 


.00233 


.44672 


.89467 


.46226 


.88674 


.47767 


.87854 


.49293 


.87007 


28 


33 


.43130 


.90221 


.44698 


.89454 


.46252 


.88661 


•47793 


.87840 


.49318 


.8699.1 


27 


34 


.43156 


.90208 


.44724 


.89441 


.46278 


.88647 


.47818 


.87826 


.49344 


.861578 


26 


35 


.43182 


.90196 


•44750 


.89428 


.46304 


.88634 


.47844 


.87812 


.49369 


.86^64 


25 


36 


.43209 


.90183 


.44776 


.89415 


.46330 


.88620 


.47869 


.87798 


.49394 


£6949 


24 


37 


.43235 


.90171 


.44802 


.89402 


.46355 


.88607 


.47895 


.87784 


.49419 


.W935 


23 


38 


.43261 


.90158 


.44828 


.89389 


.46381 


.88593 


.47920 


.87770 


.49445 


J6921 


22 


39 


.43287 


.90146 


.44854 
.44880 


.89376 


.46407 


.88580 


.47946 


.87756 


.49470 


JSi '.1 <• 


21 


40 


.43313 


.90133 


.89363 


.46433 


.88566 


.47971 


.87743 


.49495 


.•-,■-■ 


20 


41 


.43340 


.00120 


.44906 


.89350 


.46458 


.88553 


.47997 


.87729 


.49521 


.86878 


19 


42 


.43366 


.90108 


.44932 


.89337 


.46484 


.88539 


.48022 


.87715 


.49546 


.86863 


18 


43 


.43392 


.90095 


.44958 


.89324 


.46510 


.88526 


.48048 


.87701 


.49571 


.86849 


17 


44 


.43418 


.90082 


.44984 


.89311 


.46536 


.88512 


.4C073 


.87687 


.49556 


.86834 


16 


45 


.43445 


.90070 


.45010 


.89298 


.46561 


.88499 


.43099 


.87673 


.49622 


.86820 


IS 


46 


.43471 


.90057 


.45036 


.89285 


.465S7 


.8? 4 8 5 


.43124 


.87659 


.49647 


.86805 


14 


3 


.43497 


.90045 


.45062 


.89272 


.46613 


.83472 


.48150 


.87645 


.45672 


.86791 


13 


.43523 


.90032 


.45088 


.89259 


.46639 


.83458 


.48175 


.87631 


.49697 


.86777 


12 


49 


.43549 


.90019 


.45"4 


.89245 


.46664 


.88445 


.43coi 


.87617 


.49723 


.86762 


11 


50 


•43575 


.90007 


.45140 


.89232 


.46690 


.88431 


.43226 


.87603 


.49748 


.86748 


10 


51 


.43602 


.89994 


.45166 


.89219 


.46716 


.88417 


.43252 


.87589 


•49773 


.86733 


9 


52 


.43628 


.89981 


.45192 


.89206 


.46742 


.88404 


.48277 


.87575 


.49798 


.86719 


8 


53 


.43654 


.89968 


.45218 


.89193 


.46767 


.•88390 


.48303 


.87561 


.45824 


.86704 


7 


54 


.43680 


.89956 


.45243 


.89180 


.46793 


.88377 


.48328 


.87546 


.49849 


.86690 


6 


*§ 


.43706 


.89943 


.45269 


.89167 


.46819 


.88363 


.48354 


.87532 


.49874 


.86675 


5 


s6 


.43733 


.89930 


.45295 


.89153 


.46844 


.88349 


.48379 


.87518 


.49899 


.86661 


4 


57 


.43759 


.89918 


.45321 


.89140 


.46870 


.88336 


.48405 


.87504 


.49924 


.86646 


3 


58 


.43785 


.89905 


.45347 


.89127 


.46896 


.88322 


.48430 


.87490 


.49950 


.86633 


2 


59 


.43811 


.89892 


.45373 


.89114 


.46921 


.88308 


.48456 


.87476 


•49975 


.86617 


1 


60 


.43837 


.89879 


•45399 


.89101 


.46947 


.88295 


.48481 


.87462 


.50000 


.86603 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


64 


6; 


5° 


6: 


,0 


6i 





6c 


)° 



io4 



BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES 



/ 


30° 


3^ 


[° 


32° 


33° 


34° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 





.50000 


.86603 


.51504 


.85717 


.52992 


.84805 


.54464 


.83867 


.55919 


i%} 


60 


X 


.50025 


.86588 


.51529 


.85702 


.53017 


.84789 


.54488 


•532 s1 


.55943 
.55968 


3 


J 


.50050 


.86573 


.51554 


.85687 


.53041 


.84774 


.54513 


.83835 


.82871 


3 


.50076 


.86559 


•51579 


.85672 


.53066 


.84759 


.54537 


.83819 


.55992 


.82855 


57 


4 


.50101 


.86544 


.51604 


.85657 


.53091 


.84743 


.54561 


.83804 


.56016 


.82839 


56 


5 


.50126 


.86530 


.51628 


.85642 


.53115 


.84728 


.54586 


.83788 


.56040 


.82822 


55 


6 


.50151 


.86515 


.51653 


.85627 


.53140 


.84712 


.54610 


.83772 


.56064 


.82806 


54 


7 


.50176 


.86501 


.51678 


.85612 


.53164 


.84697 


.54635 


.83756 


.56088 


.82790 


53 


8 


.50201 


.86486 


.51703 


.85597 


.53189 


.84681 


.54659 
.54683 
.54708 


.83740 


.56112 


.82773 


52 


9 


.50227 


.86471 


.51728 


.85582 


.53214 


.84666 


.83724 


.56136 


.82757 


51 


10 


.50252 


.86457 


.51753 


.85567 


.53238 


.84650 


.83708 


.56160 


.82741 


50 


ii 


.50277 


.86442 


.51778 


.85551 


.53263 


.84635 


.54732 


.83692 


.56184 


.82724 


49 


12 


.50302 


.86427 


.51803 


.85536 


.53288 


.84619 


.54756 
.54781 


.83676 


.56208 


.82708 


48 


13 


.50327 


.86413 


.51828 


.85521 


.53312 


.84604 


.83660 


.56232 


.82692 


47 


14 


.50352 


.86398 


.51852 


.85506 


.53337 


.84588 


.54805 


.83645 


.56256 
.56280 


.82675 


46 


15 


.50377 


.86384 


.51877 


.85491 


.53361 


.84573 


.54829 


.83629 


.82659 


45 


16 


.50403 


.86369 


.51902 


.85476 


.53386 


.84557 


.54854 


.83613 


.56305 


.82643 


44 


17 


.50428 


.86354 


.51927 


.85461 


.534" 


.84542 


.54878 


.83597 
.83581 


.56329 


.82626 


43 


18 


.50453 
.50478 


.86340 


.51952 


.85446 


.53435 


.84526 


.54902 


.56353 


.82610 


42 


19 


.86325 


.51977 


.85431 


.53460 


.845" 


.54927 


.83565 


.56377 


.82593 


41 


20 


.50503 


.86310 


.52002 


.85416 


.53484 


.84495 


.54951 


.83549 


.56401 


•82S7f 


40 


21 


.50528 


.86295 
.86281 


.52026 


.85401 


.53509 


.84480 


.54975 


.83533 


.56425 


Jji6f 


39 


22 


.50553 


.S2051 


•8S385 


.53534 


.84464 


.54999 


.83517 


.56449 


.82544 


38 


23 


.50578 


.86266 


.52076 


.85370 


.53558 
.53583 


.84448 


.55024 


.83501 


.56473 


.82528 


37 


24 


.50603 
.50628 


.86251 


.52101 


.85355 


.84433 


.55048 


.83485 


.56497 


.S2511 


36 


*5 


.86237 


.52126 


.85340 


.53607 


.84417 


.55072 


.83469 


.56521 


.82495 


35 


26 


.50654 


.86222 


.52151 


.85325 


.53632 


.84402 


.55097 


.83453 


.56545 


,8^78 


34 


27 


.50679 


.86207 


.52175 


.85310 


.53656 


.84386 


.55121 


.83437 


.56569 


.8 246 2 


33 


28 


.50704 


.86192 


.52200 


.85294 


.53681 


.84370 


.55145 


.83421 


.56593 


.82446 


32 


29 


.50729 


.86178 


.52225 


.85279 


.53705 


.84355 


.55169 


.83405 


.56617 


■*-4-V 


31 


30 


•50754 


.86163 


.52250 


.85264 


•53730 


.84339 


.55194 


.83389 


.56641 


■ S^U 


30 


31 


.50779 
.50804 


.86148 


.52275 


.85249 


.53754 


.84324 


.55218 


.83373 


.56665 


.82396 


29 


32 


.86133 


.52299 


.85234 


.53779 


.84308 


.55242 


.83356 


.56689 


.82380 


28 


33 


.50829 


.86119 


.52324 


.85218 


.53804 


.84292 


.55266 


.83340 


.56713 


.82363 


27 


34 


.50854 


.86104 


.52349 


.85203 


.53828 


.84277 


.55291 


.83324 


.56736 


.82347 


26 


35 


.50879 


.86089 


.52374 


.85188 


.53853 


.84261 


.55315 


.83308 


.56760 


.82330 


25 


36 


.50904 


.86074 


.52399 


.85173 


.53877 


.84245 


.55339 


.83292 


.56784 


.82314 


24 


% 


.50929 


.86059 


.52423 
.52448 


.85157 


.53902 


.84230 


.55363 


.83276 


.56808 


.82297 


S3 


.50954 


.86045 


.85142 


.53926 


.84214 


.55388 


.83260 


.56832 


.82281 


22 


39 


.50979 


.86030 


.53473 


.85127 


•53951 


.84198 


.55412 


.83244 


.56856 


.82264 


21 


40 


.51004 


.86015 


.52498 


.85112 


•53975 


.84182 


.55436 


.83228 


.56880 


.82248 


20 


41 


.51029 


.86000 


.52522 


.85096 


.54000 


.84167 


.55460 


.83212 


.56904 


.82231 


19 


42 


.51054 


.85985 


.52547 


.85081 


.54024 


.84151 


.55484 


.83195 


.56928 


.82214 


18 


43 


.51079 


.85970 


.52572 


.85065 


.54049 


.84135 


.55509 


.83179 


.56952 


.82198 


17 


44 


.51104 


.85956 


.52597 


.85051 


.54073 


.84120 


.55533 


.83163 


.56976 


.82181 


16 


45 


.5x129 


.85941 


.52621 


.850:5 


.54097 


.84104 


•55557 


.83147 


.57000 


.82165 


15 


46 


.51154 


.85926 


.52646 


.85020 


.54122 


.84088 


•55S8i 


.83131 


•57024 


.82148 


14 


47 


.5"79 


.859" 


.52671 


.85005 


.54146 


.84072 


.55605 


.83ns 


•57047 


.82132 


13 


48 


.51204 


.85896 


.52696 


.84989 


.54171 


.84057 


.55630 


.83098 


.57071 


.82115 
.82098 
.82082 


12 


49 


.51229 


.85881 


.52720 


.84974 


.54195 


.84041 


.55654 


.83082 


.57095 


11 


50 


•51254 


.85866 


.52745 


.84959 


.54220 


.84025 


.55678 


.83066 


.57119 


10 


51 


.51279 


.85851 


.52770 


.84943 


,.54244 


.84009 


•55702 


.83050 


.57143 


.82065 
.82048 


9 


52 


.51304 


.85836 


.52794 


.84928 


.54269 


.83994 


.55726 


.83034 


.57167 


8 


53 


.51329 


.85821 


.52819 


.84913 


.54293 


.83978 


.55750 


.83017 


.57191 


.82032 


7 


54 


.51354 


.85806 


.52844 


.84897 


.54317 


.83962 


.55775 


.83001 


.57215 
.57238 


.82015 


6 


55 


.51379 


.85792 


.52869 


.84882 


.54342 


.83946 


.55799 


.82985 


.81999 


5 


56 


.51404 


.85777 


.52893 


.84866 


.54366 


.83930 


.55823 


.82969 


.57262 


.81982 


4 


Ii 


.51429 


.85762 


.52918 


.84851 


.54391 


.83915 


.55847 


.82953 


.57286 


.81965 


3 


.51454 


.85747 


.52943 


.84836 


.54415 


.83899 


.55871 


.82936 


•57310 


.81949 


2 


59 


•51479 


.85732 


.52967 


.84820 


.54440 


.83883 


.55895 


.82920 


•57334 


.81932 


1 


60 


.51504 


.85717 


.52992 


.84805 


.54464 


.83867 


.55919 


.82904 


.57358 


.81915 


*0 


/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


5< 


f 


5* 


S° 


5; 


7° 


5< 


>° 


5. 


5° 



BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES 



'OS 



/ 


35° 


36° 


37° 


38° 


39° 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 





.57358 
.57381 


.81915 
.81899 


.58779 
.5 802 


.8090a 


.6018a 


.79864 


.61566 


.78801 


.62932 


•77715 


60 


I 


.80885 


.60205 
.60228 


.79846 


.61589 


.78783 


.62955 


.77696 


% 


a 


.57405 


.81882 


.5826 


.80867 


.79829 


.61612 


.78765 


.62977 


.77678 


3 


.57429 


.81865 
.81848 


.58C49 


.80850 


.60251 


.79811 


.61 J35 


.78747 


.63000 


.77660 


57 


4 


.57453 


.58873 


.80833 


.60274 


.79793 


.61658 


.78729 


.6302a 


.77641 


56 


5 


•57477 


.8183a 


.58896 


.80816 


.60298 


.79776 


.61681 


.787" 


.63045 
.63068 


.77623 


55 


6 


.57501 


.81815 
.81798 


.58920 


.80799 


.60321 


.79758 


.61704 


.78694 


.77605 


54 


I 


.57524 


.58943 


.80782 


.60344 


.79741 


.61726 


.78676 


.63090 


.77586 


53 


.57548 


.81782 


.58967 


.80765 

.80748 


.60367 


.79723 


.61749 


.78658 


.63113 


.77568 


52 


9 


.57572 


.81765 
.81748 


.58990 


.60390 


.79706 


.61772 


.78640 


.63135 
.63158 


.77550 


51 


10 


•57596 


•59014 


.80730 


.60414 


.79688 


.6x795 


.7862a 


•77S3X 


50 


ii 


.57619 


.81731 


.50037 


.80713 


.60437 


.79671 


.61818 


.78604 


.63180 


.77513 


% 


ia 


.57643 


.81714 


.59061 


.80696 


.60460 


.79653 


.61841 


.78586 


.63303 


.77494 


13 


.57667 


.81698 


.50084 


.80679 


.60483 


.79635 
.79618 


.61864 


.78568 


.63225 
.63348 


.77476 


47 


14 


.57691 


.81681 


.59108 


.80662 


.60506 


.61887 


.78550 


.77458 


46 


15 


.57715 
.57738 


.81664 


.59131 


.80644 


.60529 


.79600 


.61909 


.•78532 


.63271 


.77439 


45 


16 


.81647 


.59154 


.80627 


.60553 


.79583 


.61932 


.78514 


.63293 


.77421 


44 


l l 


.57762 


.81631 


.59178 


.80610 


.60576 


.79565 


.61955 


.78496 


.63316 


.77402 


43 


18 


.57786 


.81614 


.59201 


.80593 


.60599 


.79547 


.61978 


.78478 


.63338 


.77384 


42 


19 


.57810 


fis 


.59225 
.59248 


.80576 


.60622 


.79530 


.62001 


.78460 


.63361 


.77366 


41 


20 


.57833 


.80558 


.60645 


.795" 


.62034 


.78442 


.63383 


.77347 


40 


31 


.57857 
.57881 


.81563 


.59272 


.80541 


.60668 


.79494 


.62046 


.78424 


.63406 


.77329 


39 


33 


.81546 


.59295 
.59318 


.80524 


.60691 


.79477 


.62069 


.78405 


.63428 


.77310 


38 


^3 


.57904 


.81530 


.80507 


.60714 


•79459 


.62092 


.78387 


.63451 


.77292 


37 


24 


.57928 


.81513 


.59342 


.80489 


.60738 


.79441 


.62115 
.62138 


.78369 


.63473 


.77273 


36 


as 


.57952 


.81496 


.59365 


.80472 


.60761 


.79424 


.78351 


.63496 


.77255 


35 


26 


.57976 


.81479 


.59389 


.80455 


.60784 
.60807 


.79406 


.62160 


.78333 


.63518 


.77236 


34 


fs 


.57999 


.81462 


.59412 


.80438 


.79388 


.62183 


.78315 


.63540 


.77218 


33 


.58023 


.81445 
.81428 


.59436 


.80420 


.60830 


•79371 


.62206 


.78297 


.63563 


.77199 


32 


29 


.58047 


.59459 
.5948a 


.80403 


.60853 


•79353 


.62229 


.78279 


.63585 
.63608 


.77i8i 


31 


30 


.58070 


.8141a 


.80386 


.60876 


.79335 


.62251 


.78261 


.77162 


30 


31 


.58094 


£3 


.59506 


.80368 


.60899 


.79318 


.62274 


.78243 


.63630 


.77144 


% 


32 


.58118 


.59529 


.80351 


.60922 


•79300 


.62297 


.78225 


.63653 


.77125 


33 


.58141 


.81361 


.59552 


.80334 


.60945 
.60968 


.79282 


.62320 


.78206 


.63675 
.63698 


:83 


27 


34 


.58165 


.81344 


.59576 


.80316 


.79264 


.62342 


.78188 


36 


35 


.58189 


.81327 


•59599 


.80299 


.60991 


.79247 


.62365 


.78170 


.63720 


.77070 


25 


36 


.5821a 


.81310 


.59622 


.80282 


.61015 


.79229 


.62388 


.78152 


.63742 


.77051 


24 


3 2 


.58236 


.81293 


.59646 


.80264 


.61038 


•792II 


.62411 


.78134 


.63765 


.77033 


23 


38 


.58260 


.81276 


.59669 


.80247 


.61061 


.79193 


.62433 


.78116 


.63787 


.77014 


32 


39 


.58283 


.81259 


.59693 


.80230 


.61084 


.79176 


.62456 


.78098 


.63810 


.76996 


21 


40 


.58307 


.81242 


.597i6 


.8021a 


.61107 


.79158 


.62479 


.78079 


.63832 


.76977 


30 


41 


.58330 


.81225 
.81208 


.59739 


.80195 
.80178 


.61130 


.79140 


.62502 


.78061 


.63854 


.76959 


\l 


42 


.58354 


.59763 


.61153 


•79122 


.62524 


.78043 


.63877 


.76940 


43 


.58378 


.81191 


.59786 


.80160 


.61176 


.79105 


.62547 


.78025 


.63899 


.76921 


17 


44 


.58401 


.81174 


.59809 


.80143 


.61199 


.79087 


.62570 


.78007 


.63923 


.76903 


16 


45 


.58425 


.81157 


.59832 


.80125 


.61222 


.79069 


.62593 


.77988 


.63944 


.76384 


15 


46 


.58449 


.81140 


.59856 


.80108 


.61245 


.79051 


.62615 
.62638 


.77970 


.63966 


.76866 


14 


47 


.58472 


.81123 


.59879 


.80091 


.61268 


.79033 


•77952 


.63989 


.76847 


13 


48 


.58496 


.81106 


.59902 


.80073 


.61291 


.79016 


.62660 


.77934 


.64011 


.76828 


12 


49 


.5S519 


.81089 


.50926 


.80056 


.61314 


.78998 


.62683 


.77916 


.64033 


.763io 


11 


50 


.58543 


.8x072 


•59949 


.80038 


.61337 


.78980 


.62706 


.77897 


.64056 


.76791 


10 


51 


.58567 


.81055 


•59972 


.80021 


.61360 


.78962 


.62728 


.77879 


.64078 


.76772 


9 


52 


.58590 


.81038 


.59995 


.80003 


.61383 


.78944 


.62751 


.77861 


.64100 


.76754 


8 


53 


.58614 


.81021 


.60019 


.79986 


.61406 


.78926 


.62774 


.77843 


.64123 


.76735 


7 


54 


.58637 


.81004 


.60042 


.79968 


.61429 


.78908 


.62796 


.77824 


.64145 


.76717 


6 


55 


.58661 


.80987 


.60065 


•79951 


.61451 


.78891 


.62819 


.77806 


.64167 


.76698 


5 


56 


.58684 


.80970 


.60089 


.79934 


.61474 


.78873 


.62842 


.77788 


.64190 


.76679 


4 


57 


.58708 


.80953 


.60112 


.79916 


.61497 


.78855 


.62864 


.77769 


.64212 


.76661 


3 


58 


.58731 


.80936 


.60135 


.79899 


.61520 


.78837 


.62887 


•77751 


.64234 


.76642 


2 


59 


.58755 


.80919 


.60158 


.79881 


.61543 


.78819 


.62909 


•77733 


.64256 


.76623 


I 


60 


.58779 


.80902 


.60182 


.79864 


.61566 


.78801 


.62932 


.77715 


.64279 


.76604 





t 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 


5< 


»° 


53° 


5- 


2° 


5 


t° 


5< 


0° 



106 BROWN & SHARPE MFG. CO. 

NATURAL SINES AND COSINES 






4c 





41 





42 





43 





44° • 


/ 


Sine 


Cotlne 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


.64279 


.76604 


.65606 


•75471 


.66913 


.74314 


.68200 


.73135 


.69466 


.71934 


60 


I 


.64301 


.76586 


.65628 


•75452 


.66935 


.74295 


.68221 


.73116 


.69487 


.71914 


59 


2 


.64323 


.76567 
.76548 


.65650 


•75433 


.66956 


.74276 


.68242 


.73006 


.69508 


.71894 


58 


3 


.64346 


.65672 


.754U 


.66978 


.74256 


.68264 


.73076 


.69529 


.71873 


57 


4 


.64368 


.76530 


.65694 


.75395 


.66999 


.74237 


.68285 


.73056 


.69549 


.71853 


56 


5 


.64390 


.76511 


.65716 


•75375 


.67021 


.74217 


.68306 


.73036 


.69570 


.71833 


55 


6 


.64412 


.76492 


.65738 


.75356 


.67043 


.74198 


.68327 


.73016 


.69591 


.71813 


54 


i 


.64435 


.76473 


.65759 


•75337 


.67064 


.74178 


.68349 


.72996 


.69612 


.71792 


53 


.64457 


.76455 


.65781 


.75318 


.67086 


.74159 


.68370 


.72976 


.69633 


.71772 


52 


9 


.64479 


76436 


.65803 


.75299 


.67107 


.74139 


.68391 


.72957 


.69654 


.71752 


51 


10 


.64501 


.76417 


.65825 


.75280 


.67129 


.74120 


.68412 


.72937 


.69675 


.7173a 


50 


II 


.64524 


.76398 


.65847 


.75261 


.67151 


.74100 


.68434 


.72917 


.69696 


.71711 


49 


12 


.64546 


.76380 


.65869 


.75241 


.67172 


.74080 


.68455 


.72897 


.69717 


.71691 


48 


13 


.64568 


.76361 


.65891 


.75222 


.67194 


.74061 


.68476 


.72877 


.69737 


.71671 


47 


14 


.64590 


.76342 


.65913 


.75203 


.67215 


.74041 


.68497 


.72857 


.69758 


.71650 


46 


IS 


.64612 


.76323 


.65935 


.75184 


.67237 
.67258 


.74022 


.68518 


.72837 


.69779 
.69800 


.71630 


45 


16 


.64635 


.76304 


.65956 


.75165 


.74002 


.68539 


.72817 


.71610 


44 


17 


.64657 


.76286 


.65978 


.75U6 


.67280 


.73983 


.68561 


.72797 


.69821 


.71590 


43 


18 


.64679 


.76267 


.66000 


.75126 


.67301 


.73963 


.68582 


.72777 


.6.842 


.71569 


42 


19 


.64701 


.76248 


.66022 


• 7SIO i 


.67323 


•73944 


.68603 


.72757 


.69:62 


.71549 


41 


20 


.64723 


.76229 


.66044 


.75088 


.67344 


.73924 


.68624 


.72737 


.69883 


.71529 


40 


21 


.64746 


.76210 


.66066 


.75069 


.67366 


•73904 


.68645 


.72717 


.69904 


.71508 


39 


22 


.64768 


.76192 


.66088 


•75050 


.67387 


•7388s 


.68666 


.72697 


.69925 


.71488 


38 


23 


.64700 


.76173 


.66109 


.75030 


.67409 


.73865 


.68688 


.72677 


.69946 


.71468 


37 


24 


.64812 


.76154 


.66131 


.7501 1 


.67430 


.73846 


.68709 


.72657 


.69966 


.71447 


36 


25 


.64834 


.76135 


.66153 


.74992 


.67452 


.73826 


.68730 


.72637 


.69987 


.71427 


35 


26 


.64856 


.76116 


.66175 


•74973 


.67473 


.73806 


.60751 


.72617 


.70008 


.71407 


34 


27 


.64878 


.76097 


.66197 


•74953 


.67495 


.73787 


.6:772 


.72597 


.70029 


.71386 


33 


28 


.64901 


.76078 


.66218 


.74934 


.67516 


.73767 


.68793 


.72577 


.70049 


.71366 


32 


29 


.64923 


.76059 


.66240 


.74915 


.67538 


.73747 


.683 1 4 


.72557 


.70070 


.71345 


31 


30 


.64945 


.76041 


.66262 


.74896 


•67559 


.73728 


.CGC35 


.72:37 


.70091 


.71325 


30 


31 


.64967 


.76022 


.66284 


.74876 


.67580 


.73708 


.68857 


.72517 


.70112 


.71305 


29 


32 


.64089 


.76003 


.66306 


.74857 


.67602 


.73688 


.68878 


.72497 


.70132 


.71284 


28 


33 


.65011 


.75984 


.66327 


.74838 


.67623 


.73669 


.68899 


.72477 


.70153 


.71264 


27 


34 


.65033 


.75965 


.66349 


.74818 


.67645 


.73649 


.68920 


.72457 


.70174 


.71243 


26 


35 


.6505S 


.75946 


.66371 


•74799 


.67666 


.73629 


.68941 


.72437 


.70195 


.71223 


25 


36 


.65077 


.75927 


.66393 


.74780 


.67688 


.73610 


.68962 


.72417 


.70215 


.71203 


24 


37 


.65100 


.75908 


.66414 


.74760 


.67709 


.73590 


.68983 


.72397 


.70236 


.71182 


23 


38 


.65122 


.75889 


.66436 


.74741 


.67730 


•73570 


.69004 


-72377 


.70257 


.71162 


22 


39 


.65144 


.75870 


.66458 


.74722 


.67752 


.73551 


.69025 


.72357 


.70277 


.71141 


21 


40 


.65166 


.75851 


.66480 


.74703 


.67773 


•73531 


.69046 


.72337 


.70298 


.7x121 


20 


41 


.65188 


.75832 


.66501 


.74683 


.67795 


.735" 


.60067 


.72317 


.70319 


.71100 


19 


42 


.65210 


.75813 


.66523 


.74664 


.67816 


•73491 


.69088 


.72297 


.70339 


.71080 


l8 


43 


•6S232 


.75794 


.66545 


.74644 


.67837 


.73472 


.69109 


.72277 


.70360 


.71059 


17 


44 


.65254 


•75775 


.66566 


.74625 


.67859 


•73452 


.69130 


.72257 


.70381 


.71039 


16 


45 


.65276 


.75756 


.66588 


.74606 


.67880 


•73432 


.69151 


.72236 


.70401 


.71019 


15 


46 


.65298 


.75738 


66610 


.74586 


.67901 


.73413 


.69172 


.72216 


.70422 


.70998 


14 


47 


.65320 


.75719 


.66632 


.74567 


.67923 


•73393 


.69193 


.72196 


.70443 


.70978 


13 


48 


.65342 


•75700 


.66653 


.74548 


.67944 


•73373 


.69214 


.72176 


.70463 


.70957 


12 


49 


.65364 


.75680 


.66675 


.74528 


.67965 


■73353 


.69235 


.72156 


.70484 


.70937 


II 


50 


.65386 


.75661 


.66697 


.74509 


.67987 


•73333 


.69256 


.72136 


.70505 


.70916 


10 


51 


.65408 


.75642 


.66718 


.74489 


.68008 


.73314 


.69277 


.72116 


.70525 


.70896 


9 


52 


.65430 


.75623 


.66740 


.74470 


.68029 


.73294 


.69298 


.72095 


.70546 


.70875 


8 


53 


.65452 


.75604 


.66762 


.74451 


.68051 


.73274 


.69319 


.72075 


.70567 


.70855 


7 


54 


.65474 


.75585 


.66783 


.74431 


.68072 


.73254 


.69340 


.72055 


.70587 


.70834 


6 


55 


.65496 


.75566 


.66805 


.74412 


.68093 


.73234 


.69361 


.72035 


.70608 


.70813 


5 


56 


.65518 


.75547 


.66827 


.74392 


.68115 


.73215 


.69382 


.72015 


.70628 


.70793 


4 


57 


.65540 


.75528 


.66848 


.74373 


.68136 


.73195 


.69403 


•71995 


.70649 


.70772 


3 


58 


.65562 


.75509 


.66870 


•74353 


.68157 


.73175 


.69424 


.71974 


.70670 


.70752 


2 


59 


.65584 


•75490 


.66891 


.74334 


.68179 


.73155 


.69445 


.71954 


.70600 


.70731 


X 


60 


.65606 


•75471 


.66913 


.743U 


.68200 


.73135 


.69466 


.71934 


.70711 .70711 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine | Sine 


/ 


4< 


?° 


4 


3° 


4; 


7° 


4< 


5° 


45° 



BROWN &. SHARPE MFG. CO. I07 

NATURAL TANGENTS AND COTANGENTS 



/ 








i° 


2 


O 


3 





4° 


/ 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 





.00000 


Infinite 


.01746 


S7.2900 


.03492 


28.6363 


.05241 


19.081 1 


.06993 


14.3007 


60 


X 


.00029 


3437.75 
1718.87 


.01775 


56.3506 


.03521 


28.3094 


.05270 


18.9755 


.07022 


14.241 1 


3 


2 


.00058 


.01804 


55.4415 


.03550 


28.1664 


.05299 


18.871 1 


.07051 


14.1821 


3 


.00087 


1x45.92 


.01833 


54.5613 


.03579 


27.9372 


.05328 


18.7678 


.07080 


14.1235 


57 


4 


.00116 


859.436 
687.549 


.01862 


53.7086 
52.8821 


.03609 
.03638 


27.7«7 


.05357 


18.6656 


.07110 


14.0655 


56 


5 


.00145 


.01891 


27.4899 


.05387 


18.5645 


.07139 
.07168 


14.0079 


55 


6 


.00175 


572.957 


.01920 


52.0807 


.03667 


27.2715 


.05416 


18.4645 


13.9507 


54 


I 


.00204 


491.106 


.01949 


51.3032 


.03696 


27.0566 


.05445 


18.3655 


.07197 


13.8940 


53 


.00233 


429.718 


.01978 


50.5485 
49.8157 


.03725 


26.8450 


.05474 


i l'*n 


.07227 


13.8378 


52 


9 


.00262 


381.971 


.02007 


.03754 
•03783 


26.6367 


.05503 


18.1708 


.07256 
.07285 


13.7821 


51 


10 


.00291 


343-774 


.02036 


49.1039 


26.4316 


.05533 


18.0750 


13.7267 


50 


II 


.00320 


312.521 


.02066 


48.4121 


.03812 


26.2296 


.05562 


17.9802 


.07314 


13.6719 


49 


1a 


.00349 


286.478 


.02095 


477395 


.03842 


26.0307 


.05591 


17.8863 


.07344 


13.6174 


43 


13 


.00378 


264.441 


.02124 


47.0853 


.03871 


25.8348 


.05620 


17.7934 


.07373 


13.S634 


47 


14 


.00407 


245.552 
229.182 


.02153 


46.4489 


.03900 


25.6418 


.05649 


17.7015 


.07402 


13.5098 


46 


15 


.00436 


.02182 


45.8294 


.03929 
.03958 


25.4517 


.05678 


17.6106 


.07431 


134566 


45 


16 


.00465 


214.858 


.02211 


452261 


25.2644 


.05708 


17.5205 


.07461 


134039 


44 


2 


.00495 


202.219 


.02240 


44.6386 


.03987 


25.0708 


.05737 


17.4314 


.07490 


13.3515 


43 


.00524 


190.984 


.02269 


44.0661 


.04016 


24.8978 


.05766 


17.3432 


.07519 


13.2996 
13.2480 


42 


19 


.00553 


180.932 
171.885 


.02298 


43.5081 


.04046 


24.7185 


.05795 


17.2558 


.07548 


41 


20 


.00582 


.02328 


42.9641 


.04075 


24.5418 


.05824 


17.1693 


.07578 


131969 


40 


21 


.00611 


163.700 


.02357 
.02386 


42.4335 


.04104 


24.3675 


.05854 
.05883 


17.0837 


.07607 


13.1461 


39 


22 


.00640 


156.259 


41.9158 


.04133 


24.1957 


16.9990 


.07636 


13.0958 


38 


-3 


.00669 
.00698 


149.465 


.02415 


41.4106 


.04162 


24.0263 


.05912 


16.9150 


.07665 


13.0458 


37 


*4 


143237 


.02444 


40.9174 


.04191 


23.8593 


.05941 


16.8319 


.07695 


12.9962 


36 


»5 


.00727 


137-507 


.02473 


40.4358 


.04220 


23.6945 


.05970 


16.7496 


.07724 


12.9469 


35 


26 


.00756 


132.219 


.02502 


39.0655 


.04250 


23.5321 


.05999 


16.6681 


.07753 


12.8981 


34 


27 


.00785 


127.321 


.02531 


39.5059 


.04279 


23.3718 


.06029 


16.5874 


.07782 


12.8496 


33 


28 


.C0815 


X22.774 


.02560 


39.0568 


.04308 


23.2137 


.06058 


16.5075 


.07812 


12.8014 


32 


29 


.00844 


1x8.540 


.02589 


38.6177 


.04337 


23.0577 


.06087 


16.4283 


.07841 


12.7536 


31 


30 


.00873 


114.589 


.02^19 


38.1885 


.04366 


22.9038 


.06116 


16.3499 


.07870 


12.7062 


30 


31 


.00902 


x 10.892 


.02648 


37.7686 


.04395 


22.7519 


.06145 


16.2722 


.07899 


12.6591 


29 


32 


.00931 


107.426 


.02677 


37-3579 


.04424 


22.6020 


.06175 


16.1952 


.07929 
.07958 


12.6124 


28 


33 


.00960 


104-171 


.02706 


36.9560 


.04454 


22.4541 


.06204 


16.1190 


12.5660 


27 


34 


.00989 


101.107 


.02735 


36.5627 


.04483 


22.3081 


.06233 


16.043s 


.07087 


12.5199 


26 


33 


.01018 


98.2179 


.O2764 


36.1776 


.04512 


22.1640 


.06262 


is.9687 


.08017 


12.4742 


25 


36 


.01047 


95.4895 


.02793 
.02822 


35.8006 


.04541 


22.0217 


.06291 


15.8945 


.08046 


12.4288 


24 


37 


.01076 


92.9085 


35.4313 


.04570 


21.8813 


.06321 


15.821 1 


.08075 


12.3838 


23 


38 


.01:05 


90.4633 


.O285X 
.02881 


35.0695 


.04599 


i I.7426 


.06350 


15.7483 


.08104 


12.3390 


22 


39 


.01135 


83.1436 


34.7151 


.04628 


21.6056 


.06379 
.06408 


15.6762 


.08134 


12.2946 


21 


40 


.01164 


85.9398 


.02910 


34.3678 


.04658 


21.4704 


15.6048 


.08163 


12.2505 


20 


41 


.01193 


83.8435 


.02939 


34.0273 


.04687 


21.3369 


.06437 


15.5340 
15.4638 


.08192 


12.2067 


\l 


42 


.01222 


81.8470 


.02968 


33.6935 


.04716 


21.2049 


.06467 


.08221 


12.1632 


43 


.01231 


79.9434 
78.1263 


.02997 


33.3662 


.04745 


21.0747 


.06496 


15.3943 


.08251 
.08280 


12.1201 


17 


44 


.01280 


.03026 


33.0452 


.04774 


20.9460 


.06525 


15.3254 


12.0772 


16 


45 


.01309 


76.3900 


.03055 


32.7303 


.04803 


20.8188 


.06554 
.06584 


15.2571 
15.1893 


.08309 


12.0346 


15 


46 


.01333 


74.7292 


.O3084 


32.4213 


.04833 


20.6932 


.08339 
.08368 


11.9923 


14 


47 


.01367 


73.1350 


.03114 


32.1181 


.04862 


20.5691 


.06613 


15.1222 


11.9504 


13 


48 


.01396 


71.6151 


.03143 


31.8205 


.04891 


20.4465 


.06642 


15.0557 


.08397 


11.9087 


12 


49 


.014=5 


70.1533 


.03172 


31.5284 


.04920 


20.3253 


.06671 


14.9898 


.08427 


11.8673 


II 


SO 


•01455 


68.7501 


.03201 


31.2416 


.04949 


20.2056 


.06700 


14.9244 


.08456 


11.8262 


10 


SI 


.01484 


67.4019 


.03230 


30.9599 


.04978 


20.0872 


.06730 


14.8596 


.08485 


n.7853 
11.7448 


9 


52 


.01513 


66.1055 
64.8580 


.03259 


30.6833 


.05007 


19.9702 


.06759 


14.7954 


.08514 


8 


53 


.01542 


.C3288 


30.4116 


.05037 


19.8546 


.06788 
.06817 


u.7317 


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108 BROWN & SHARPE MFG. CO. 

NATURAL TANGENTS AND COTANGENTS 



/ 


5° 


6 





7 





8° 


9 





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BROWN & SHARPE MFG. CO. 109 

NATURAL TANGENTS AND COTANGENTS 



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IO° 


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[° 


12° 


13° 


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.24254 


4.12301 


.26110 


3.82992 


22 


39 


.18805 


5.31778 


.206l8 


4.85013 


.22444 


4.45548 


.24285 


4.11778 


.26141 


382537 


21 


40 


.1883S 


5.30928 


.20648 


4.84300 


.22475 


4.44942 


.24316 


4.11256 


.26172 


3.82083 


20 


41 


.18865 


5.30080 


.20679 


4.83590 


.22505 


4.44338 


.24347 


4.10736 


.26203 


3.8x630 


:s 


42 


.18895 


5.29235 


.20709 


4.82882 


.22536 


4-43735 


.24377 
.24408 


4.10216 


.26235 


3.81177 


43 


.18925 


5.28393 


•20739 


4.82175 


.22567 


4.43134 


4.00690- 


.26266 


3.80726 


17 


44 


.18955 


5-27553 


.20770 


4.81471 


.22597 


442534 


.24439 


4.09182 


.26297 
.26328 


3.80276 


16 


45 


.18986 


5.26715 


.20800 


4.80769 


.22628 


4.41936 


.24470 


4.08666 


3.79827 


15 


46 


.19016 


5.25880 


.20830 


4.80068 


.22658 


4.41340 


.24501 


4.08152 


.26359 


379378 


14 


is 


.19046 


5.25048 


.2086l 


4.79370 


.22689 


4.40745 


.24532 


4.07639 


.26390 


3.78931 


13 


.19076 


5.24218 


.20891 


4.78673 


.22719 


4.40152 


.24562 


4.07127 


.26421 


3.78485 


12 


49 


.19106 


5.23391 


.20921 


4.77978 


.22750 


4.39560 


.24593 


4.06616 


.26452 
.26483 


3.78040 


IX 


50 


.19136 


5.22566 


.20952 


4.77286 


.22781 


4.38069 


.24624 


4.06107 


3-77595 


10 


51 


.19166 


5.21744 


.20982 


4.7659s 


.22811 


4.38381 


.24655 


4.05509 


.26515 


377IE2 


2 


52 


.19197 


5-20925 


.21013 


4-7S906 


.22842 


4-37793 


.24686 


4.05092 


.26546 


3.76709 


53 


.19227 


5.20107 


.21043 


4.75219 


.22872 


4.37207 


.24717 


4.04586 


.26577 
.26608 


3.76268 


7 


54 


.19257 


5. 19293 


.21073 


4.74534 


.22903 


4.36623 


.24747 


4.04081 


3.75828 


6 


55 


.19287 


5.18480 


.21104 


4.73851 


.22934 


4.36040 


.24778 


4.03578 


.26639 


3.75388 


5 


56 


.19317 


5.17671 


.21134 


4.73170 


.22964 


435459 


.24809 


4.03076 


.26670 


3.74950 


4 


57 


.19347 


5.16863 


.21164 


4.72490 


.22995 


4.34879 


.24840 


4.02574 


.26701 


3.745X2 


3 


58 


.19378 


5.16058 


.21195 


4.71813 


.23026 


4.343O0 


.24871 


4.02074 


.26733 


374075 


2 


59 


.19408 


5.15256 


.21225 


4.71137 


.23056 


4.33723 


.24002 


4-01576 


.26764 


373640 


I 


60 


.19438 


5.14455 


.21256 


4.70463 


.23087 


4.33148 


.24933 


4.01078 


.26795 


3.73205 





/ 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


/ 


7< 


7° 


7i 


1° 


7; 


7° 


7< 


l ° 


75° 



110 BROWN & SHARPE MFG. CO. 

NATURAL TANGENTS AND COTANGENTS 



/ 


15° 


16 


17° 


18 


19° 


/ 


Tans: 


Cotang: 


Tans: 


Cotang: 


Tans: 


Cotansr 


Tangr 


Cotansr 


Tang: 


Cotansr 





.26795 
.26826 


3.73205 


.28675 


3.48741 


.30573 


3-27085 


.32492 


3.07768 


•34433 


2.90421 


60 


I 


3.72771 


•^ 70 S 


3.48359 


.30605 


326745 


.32524 


3.07464 


.34465 
.34498 


2.90147 


n 


2 


.26857 
.26888 


3.72338 


.28738 


3.47977 


.30637 


3.26406 


.32556 


3.07160 


2.80873 


3 


3.71907 


.28769 


3.47596 


.30669 


3.26067 


.32588 


3.06857 


•34530 


2.89600 


57 


4 


.26920 


3.7M76 


.28800 


3.47216 


.30700 


325729 


.32621 


3.06554 


.34563 


2.89327 


56 


5 


.26951 


3.71046 


.28832 


3.46837 


.30732 


325392 


.32653 


3.06252 


.34596 


2.89055 


55 


6 


.26982 


3.70616 


.28864 


3.46458 
3.46080 


.30764 


325055 


.32685 


3.05950 


.34628 


2.88783 


54 


7 


.27013 


3.70188 


.28895 


.30796 


3.24719 


.32717 


305649 


.34661 


2.8851 1 


53 


8 


.27044 


3.69761 


.28927 
.28958 


3.45703 


.30828 


3.24383 


.32749 


305349 


.34693 


2.88240 


52 


9 


.27076 


3.69335 


3.45327 


.30860 


3.24049 


.32782 


3-05049 


.34726 


2.87970 


51 


10 


.27107 


3.68909 


.28990 


3.44951 


.30891 


3.237U 


.32814 


3.04749 


.34758 


2.87700 


50 


ii 


.27138 


3.68485 


.29021 


3.44576 


.30923 


3.23381 


.32846 


3.04450 


.34791 


2.87430 


49 


13 


.27169 


3.68061 


.29053 


3.44202 


.30955 


3.23048 


.32878 


3.04152 


.34824 


2.87161 


48 


13 


.27201 


3.67638 


.29084 


3.43829 


.30987 


3.22715 


.32911 


3.03854 


.34856 


2.86892 


47 


14 


,27232 


3.67217 


.29116 


3.43456 


.31019 


3.22384 


.32943 


3.03556 


.34889 


2.86624 


46 


15 


.27263 


3.66796 


.29147 


3.43084 


.31051 


3.22053 


.32975 


3.03260 


.34922 


2.86356 


45 


16 


.27204 


3.66376 


.29179 


3.42713 


.31083 


3.21722 


.33007 


3.02963 


.34954 


2.86089 


44 


17 


.27326 


3.65957 


.29210 


342343 


.31115 


3.21392 


.33040 


3.02667 


.34987 


2.85822 


43 


18 


% 3 M 


3.65538 


.29242 


341973 


.3"47 


3.21063 


.3307a 


3-02372 


.35020 


2.85555 


42 


19 


3.65 1 21 


.29274 


3.41604 


.3"78 


3.20734 


.33104 


3.02077 


.35052 


2.85289 


41 


20 


.27419 


3.64705 


.29305 


3.41236 


.31210 


3.20406 


.33136 


3.01783 


.35085 


2.85023 


40 


21 


.27451 
.27482 


3.64289 


.29337 


3.40869 


.31242 


3.20079 


.33169 


3.01489 


.35118 


2.84758 


39 


22 


3.63874 


.29368 


3.40502 


.31274 


3-19752 


.33201 


3.01 196 


.35150 


2.84404 


38 


23 


.27513 


3.63461 


.29400 


3.40136 


.31306 


319426 


.33233 


3.00903 


.35183 


2.84229 


37 


24 


.27545 


3.63048 


.29432 


3.39771 


.31338 


3.19100 


.33266 


3.0061 1 


.35216 


2.83965 


36 


25 


.27576 


3.62636 


.29463 


3.39406 


.31370 


3.18775 


.33298 


3.00319 
3.00028 


.35248 


2.83702 


35 


26 


.27607 


3.62224 


.29495 


3.39042 


.31402 


3.18451 


.33330 


.35281 


2.83439 


34 


27 


.27638 


3.61814 


.29526 


3.38679 


.31434 


3.18127 


.33363 


a.99738 


.35314 


2.83176 


33 


28 


.27670 


3.6140s 


.29558 


3.38317 


.31466 


3.17804 


.33395 


2.99447 


.35346 


2.82914 


32 


29 


.27701 


3.60996 


.29590 


3-37955 


.31498 


3.17481 


.33427 


2.99158 


.35379 


2.82653 


31 


30 


.27732 


3.60588 


.29621 


337594 


.31530 


3.17I59 


.33460 


2.98868 


•35412 


2.82391 


30 


31 


.27764 


3.60181 


.29653 


3.37234 


.31562 


3.16838 


•33492 


2.98580 


.35445 


2.82130 


3 


33 


.27795 


3.59775 


.29685 


3.36875 


.31594 


3.16517 


.33524 


2.^8292 


.35477 


2.81870 


33 


.27826 


3.59370 


.29716 


3.36516 


.31626 


3.16197 


•33557 


2.98004 


.355IO 


2.81610 


27 


34 


3C 


3.58966 


.29748 


3.36158 


.31658 


3.15877 


.33589 


2.97717 


•35543 


2.81350 


26 


35 


3.58562 


.29780 


3.35800 


.31690 


3.15558 


.33621 


2.97430 


.35576 


2.81091 


25 


36 


.27921 


3.58160 


.29811 


3-35443 


.31722 


3.15240 


.33654 
.33686 


2.97144 


.35608 


2.80833 


24 


37 


.27952 
.27983 
.28015 


3.57758 


.29843 


3.35087 


.31754 


314922 


2.9685S 


.35641 


2.80574 


23 


38 


3-57357 


.29875 


3-34732 


.31786 


3.14605 


.33718 


2.9657.1 


.35674 


2.80316 


22 


39 


3.56957 


.29906 


3-34377 


.31818 


3.14288 


•33751 


2.o6:&3 


.35707 


2.80059 


21 


40 


.28046 


3.56557 


.29938 


3.34023 


.31850 


3.13972 


.33783 


2.96004 


.35740 


2.79802 


20 


41 


.28077 


3.56159 


.29970 


3.33670 


.31882 


3.13656 


.33816 


2.95721 


.35772 


2.79545 


19 


42 


.28109 


3.55761 


.30001 


3.33317 


.3I9U 


3.13341 


.33848 


2.95437 


.35S05 


2.79289 


18 


43 


.28140 


35S364 


.30033 


3-32965 


.31946 


3.13027 


.33881 


2.95155 


.35338 


2.79033 


17 


44 


.28172 


3-54968 


.30065 


3.32614 


.31978 


3.12713 


.33913 


2.94872 


.35871 


2.78778 


16 


45 


.28203 


3-54573 


.30097 


3.32264 


.32010 


3.12400 


•33945 


2.94591 


.35004 


2.78523 


15 


46 


.28234 


3.54179 


.30128 


331914 


.32042 


3.12087 


.33978 


2.94309 


•35937 


2.78269 


14 


% 


.28266 


3.5378s 


.30160 


3.31565 


.32074 


3.11775 


.34010 


2.940-8 


.35909 


2.78014 


13 


.28297 


3-53393 


.30192 


3.31216 


.32106 


3.11464 


.34043 


2.93748 


.36002 


2.77761 


12 


49 


.28329 


3.53001 


.30224 


3.30868 


.32139 


3.11153 


•34075 


2.93468 


.36035 
.36068 


2.77507 


11 


50 


.28360 


3.52609 


•30255 


3.30521 


.32171 


3.10842 


.34108 


2.93189 


2.77254 


10 


51 


.28391 


3.52219 


.30287 


3.30174 


.32203 


3.10532 


.34140 


2.92910 


.361OI 


2.77002 


§ 


52 


.28423 


3.51829 


.30319 


3.29829 


•32235 


3.10223 


.34173 


2.92632 


.36134 


2.76750 


53 


.28454 


3-SI44I 


.30351 


3.29483 


.32267 


3.09914 


.34205 
.34238 


2.92354 


.36167 


2.76498 


7 


54 


.28486 


351053 


.30382 


3.29139 


.32299 


3.09606 


2.92076 


.36199 


2.76247 


6 


55 


.28517 


3.50666 


.30414 


3.28795 


.32331 


3.09298 


.34270 


2.91799 


.36232 


2.75996 


5 


56 


.28549 


3.50279 


.30446 


3.28452 


.32363 


3.08991 


.34303 


2.91523 


.36265 


2.75746 


4 


57 


.28580 


3.49894 


.30478 


3.28109 


.32396 


3.08685 


.34335 
.34368 


2.91246 


.36298 


2.75496 


3 


58 


.28612 


3.49509 


.30509 


3.27767 


.32428 


3.08379 


2.90971 


.36331 


2.75246 


a 


59 


.28643 


3-49125 


.30541 


3.27426 


.32460 


3.08073 


•34400 


2.90696 


.36364 


a.74997 
2.74748 


1 


6o 


.28675 


348741 


.30573 


3.27085 


.32492 


3.07768 


•34433 


2.90421 


.36397 





/ 


Cotang- 


Tangr 


Cot an g 


Tans: 


Cotang: 


Tans: 


Cotansr 


Tangr 


Cotansr 


Tangr 


/ 


74° 


73° 


72° 


7i° 


70° 



BROWN & SHARPE MFG. CO. 

NATURAL TANGENTS AND COTANGENTS 



/ 


20° 


21° 


22° 


23° 


24° 


/ 


Tang 


Cotang 


Tangr 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 





.36397 


2.74748 


.38386 


2.60509 


.40403 


2.47509 


.42447 


2.35585 


.44523 


2.24604 


60 


I 


.36430 


2.74499 


.38420 


2.60283 


.40436 


2.47302 


.42482 


2.35395 


.44558 


2.24428 


59 


3 


.36463 


2.74251 


.38453 


3.60057 


.40470 


2.47095 


.42516 


2.35205 


.44593 


2.24252 


58 


3 


.36496 


2.74004 


.38487 


2.50831 


.40504 


2.46888 


.42551 


2.35015 


.44627 


2.24077 


57 


4 


.36529 


2.73756 


.38520 


2.59606 


.40538 


2.46682 


.42585 


2.34825 


.44662 


2.23002 


56 


5 


.36562 


2.73509 


$8 


2.59381 


.40572 


2.46476 


.42619 


2.34636 


.44697 


2.23727 


55 


6 


.36595 


2.73263 


2.59156 


.40606 


2.46270 


.42654 


2.34447 


•44732 


2.23553 


54 


I 


.36628 


2.73017 


.38620 


2.58932 


.40640 


2.46065 


.42688 


2.34258 


.44767 


2.23378 


53 


.36661 


2.72771 


.38654 


2.58708 


.40674 


2.45860 


.42722 


2.34069 


.44802 


2.23204 


52 


9 


.36694 


2.72526 


.38687 


2.58484 


.40707 


2*45655 


.42757 


2.33881 


.44837 


2.23030 


51 


10 


.36727 


2.72281 


.38721 


2.58261 


.40741 


2.45451 


.42791 


2.33693 


.44872 


2.33857 


50 


ii 


.36760 


2.72036 


.38754 
.38787 


2.58038 


•40775 


2.45246 


.42836 


2.33505 


•44907 


2.22683 


49 


12 


.36793 


2.71792 


2.57815 


.40809 


2.45043 


.42860 


2.33JI7 


.44942 


2.22510 


48 


13 


.36826 


2.71548 


.38821 


2.57593 


.40843 


2.44839 


.42894 


2.33130 


•44977 


2.22337 


47 


14 


.36859 


2.71305 


jUS 


2.57371 


.40877 


2.44636 


.42929 


2.32943 


.45012 


2.22164 


46 


IS 


.36892 


2.71062 


2.57150 


.40911 


2.44433 


.42963 


2.32756 


.45047 


2.21992 


45 


16 


.36925 


2.70819 


.38921 


2.56928 


.40945 


2.44230 


.42998 


2.32570 


.45082 


2.21819 


44 


17 


.36958 


2.70577 


'.38988 


2.56707 


.40979 


2.44027 


.43032 


2.32383 


.45U7 


2.21647 


43 


18 


.36991 


2.7033S 


2.56487 


.41013 


2.43325 


.43067 


3.32197 


.45152 


2.21475 


42 


19 


.37024 


2.70094 


.39022 


2.56266 


.41047 


2.43623 


.43101 


2.32012 


.45187 


2.21304 


41 


ao 


.37057 


2.69853 


.39055 


2.56046 


.41081 


2.43422 


.43136 


2.31826 


.45222 


2.21132 


40 


21 


.37090 


2.69612 


.39089 


2.55827 


.41115 


2.43230 


.43170 


2.31641 


.45257 


2.20961 


39 


22 


.37123 


2.69371 


.39122 


2.55608 


.41149 


2.43019 


.43205 


2.31456 


.45292 


2.20790 


38 


23 


.37157 


2.69131 


.39156 


2.55389 


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2.68892 


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2.55170 


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2.42618 


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2.31086 


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34 


27 


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32 


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21 


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2.16255 


II 


50 


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2.49597 


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2.3731 x 


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2.26196 


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2.15925 


| 


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2.49177 


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2.37"8 


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2.15432 




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59 


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/ 


Cotang 


Tang 


Cotang- 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


t 


6< 


)° 


6* 


1° 


67° 


66° 


65° 



112 BROWN *. SHARPE MFG. CO. 

NATURAL TANGENTS AND COTANGENTS 



/ 


2f 


O 


26° 


27° 


28° 


29 


/ 


Tang 


Cotang 


Tans: 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 





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60 


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59 


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57 


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55 


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38 


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37 


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35 


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a 


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/ 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


/ 


6, 


\° 


6. 


j° 


6: 


2° 


6 


1° 


6 


0° 



BROWN & SHARPE MFG. CO. 1 13 

NATURAL TANGENTS AND COTANGENTS 



1 


3o° 


31° 


32° 


33° 


34° 


1 


Tang: 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 





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a 


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57 


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56 


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55 


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/ 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


/ 


59° 


5! 


1° 


5; 


7° 


5< 


5° 


5 


5° 



H4 



BROWN & SHARPE MFG. CO. 



NATURAL TANGENTS AND COTANGENTS 



/ 


35° 


36° 


37° 


38° 


39° 


1 


Tans: 


Cotang: 


Tangr 


Cotang: 


Tangr 


Cotang: 


Tangr 


Cotang: 


Tangr 


Cotang: 





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1.42726 


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53 


.72344 


I.38229 


.75037 


1.33268 


.77801 


1.28533 


.80642 


I.24005 


.83564 


1. 19669 


7 


54 


.72388 


I.38I45 


.75082 


1. 33187 


.77848 


1.28456 


.80690 


I. 2393 1 


.83613 


X. 19599 


6 


55 


.72432 


I.38060 


.75128 


1.33107 


.77895 


1.28379 


.80738 


1.23858 


.83662 


x. 19528 


5 


56 


-72477 


1.37976 


.75173 


1.33026 


.77941 


1.28302 


.80786 


I.23784 


.83712 


1.19457 


4 


57 


.72521 


1. 37891 


.75219 


1.32Q46 


.77988 


1.28225 


.80834 


I.23710 


.83761 


I. I 9387 


3 


58 


.72565 


1.37807 


.75264 


1.32865 


.78035 


1. 28148 


.80882 


I.23637 


.83811 


1. 19316 


a 


59 


.72610 


1.37722 


.753io 


1.32785 


.78082 


1. 2807 1 


.80930 


I.23563 


.83860 


I. 19246 


1 


6o 


.72654 


1.37638 


.75355 


1.32704 


.78129 


1.27994 


.80978 


1.23490 


.83910 


1.19175 





/ 


Cotang 


Tang 


Cotang: 


Tang: 


Cotang 


Tang: 


Cotang: 


Tangr 


Cotang: 


Tang: 


/ 


5' 


i° 


5: 


i° 


5: 


,0 


Si° 


5< 


0° 



BROWN & SHARPE MFG. CO. I 15 

NATURAL TANGENTS AND COTANGENTS 



# 


40° 


4 


i° 


42° 


43° 


44° 


/ 


Tang: 


Cotang: 


Tang: 


Cotang: 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 





.83910 


1.19175 


.86929 


1.15037 


.90040 


1.11061 


.93252 


1.07237 


.96569 


1.03553 


60 


I 


.83960 


1.19105 


.86980 


1. 14969 


.90093 


1.10996 


.93306 


1. 07174 


.96625 


x. 03493 


59 


a 


.84009 


1.19035 


.87031 
.87082 


1. 14902 


.90146 


1.10931 


.93360 


1.07112 


.96681 


1.03433 


58 


3 


.84059 


1.18964 


1.14834 


.90199 


1.10867 


.93415 


1.07049 


.96738 


1.03372 


57 


4 


.84108 


1.18894 


.87133 


1. 14767 


.90251 


1. 10802 


.93469 


1.06987 


.96794 


1. 0331 3 


56 


I 


.84158 


1.18824 


.87184 


1.14699 


.90304 


1.10737 


.93524 


1.06925 


.96850 


1.03252 


55 


.84208 


1. 18754 
1. 18684 


.87236 


1.14632 


.90357 


x. 10672 


.93578 


x. 06862 


.96907 


1. 03192 


54 


I 


.84258 


.87287 


1.1456s 


.90410 


x. 10607 


.93633 


1.06800 


.96963 


1.03133 


53 


.84307 


1.18614 


.87338 


1. 14498 


.00463 


1. 10543 


.93688 


1.06738 


.97020 


1.03072 


52 


9 


.84357 


1.18544 


.87389 


1. 14430 


.90516 


1.10478 


.93742 


1.06676 


.97076 


1. 0301 2 


51 


10 


.84407 


1.18474 


.87441 


1.14363 


.90569 


1.10414 


•93797 


1.06613 


.97133 


x. 02952 


50 


II 


.84457 


1. 18404 


.87492 


1. 14296 


.90621 


1. 10349 


.93852 


1.06551 
1.06489 


.97189 


x. 02892 


49 


u 


.84507 


1. 18334 


.87543 


1. 14229 


.90674 


1. 10285 


.93906 


.97246 


1.02832 


48 


13 


.84556 


1. 18264 


.87595 


1.14162 


.90727 


1. 10220 


.93961 


1.06427 


.97302 


1.02772 


47 


14 


.84606 


1.18104 


.87646 


1.14095 


.90781 


x.10156 


.94016 


1.06365 


.97359 


x. 02713 


46 


IS 


.84656 


1.18125 


.87698 


1. 1 4028 


.90834 


1.10091 


.94071 


1.06303 


.97416 


1.02653 


45 


16 


.84706 


1.18055 


.87749 


1.13961 


.90887 


1. 10027 


.94125 


1. 0624 1 


.97472 


1.02593 


44 


2 


.84756 
.84806 


1.17986 


.87801 


1.13894 


.90940 


1.09963 


.94180 


1.06179 


.97529 


1.02533 


43 


1.17916 


.87852 


1. 13828 


.90993 


1.09399 


.94235 


x.06117 


.97586 


1.02474 


42 


J9 


.84856 


1. 1 7846 


.87904 


1.13761 


.91046 


1.09834 


.94290 


1.06056 


.97643 


1.02414 


41 


20 


.84906 


I.I7777 


.87955 


1. 13694 


.91099 


1.09770 


•94345 


1.05994 


.97700 


1.02355 


40 


21 


.84956 


1. 17708 


.88007 


1.13627 


.9"53 


1.09706 


.94400 


1.05932 


.97756 


x. 02295 


39 


22 


.85006 


1. 1 7638 


.88059 


1.13561 


.91206 


1.09643 


•94455 


x. 05870 


.97813 


x. 02236 


38 


33 


.85057 


1. 17569 


.88110 


1. 13494 


.91259 


1.09578 


.94510 


1.05809 


.97870 


1. 021 76 


37 


24 


.85107 


x. 17500 


.88162 


1. 134 28 


.91313 


1. 09514 


.94565 


1.05747 


.97927 


1.021 17 


36 


35 


.85157 


1. 17430 


.88214 


1.13361 


.91366 


1.09450 


.94620 


1.05685 


.97984 


x. 02057 


35 


26 


.85207 


1.17361 


.88265 


1. 13295 
1. 1 3228 


.91419 


1.09386 


.94676 


1.05624 


.98041 


1. 01998 


34 


% 


.85257 


1. 1 7292 


.88317 


.91473 


1.09322 


.94731 


1.05562 


.98098 


1. 01939 


33 


.85308 


1. 1 7223 


.88369 


1.13x62 


.91526 


1.09258 


.94786 


I. 05501 


.98155 


x. 01879 


32 


29 


.85358 


1.17154 


.88421 


1. 13096 


.91580 


1. 09195 


.94841 


1.05439 
1.05378 


.98213 


1.01820 


31 


30 


.85408 


1.17085 


.88473 


1. 13029 


.91633 


1.09131 


.94896 


.98270 


i. 01 761 


30 


3i 


.85458 


1. 17016 


.88524 


1.12963 


.91687 


1.09067 


.94952 


1.05317 


.98327 


1. 01 702 


3 


32 


.85509 


1. 16947 


.88576 


x. 12897 


.91740 


1.09003 


.95007 


1.05255 


.98384 


x. 01642 


33 


.85559 


1.16878 


.88628 


1.12831 


.91794 


1.08940 


.95063 


I. OS 1 94 


.98441 


i. 01 583 


27 


34 


.85609 


1. 16809 


.88680 


1. 1 2765 


.91847 


1.08876 


.95"8 


1.05133 


.98499 


i. 01 524 


26 


35 


.85660 


1.16741 


.88732 


1. 12699 


.91901 


1.08813 


.95173 


I.05072 


.98556 


I.OX465 


25 


36 


.85710 


1. 16672 


.88784 


1.12633 


.91955 


1.08749 


.95229 


1. 05010 


.98613 


I.0I4O6 


24 


3 


.85761 


1. 16603 


.88836 


1.12567 


.9^008 


1.08686 


.95284 


1.04949 


.98671 


1.01347 

1. 01 288 


23 


.85811 


1.16535 


.88888 


1. 1 2501 


.92062 


1.08622 


•95340 


x. 04888 


.98728 


22 


39 


.85862 


1. 16466 


.88940 


1. 1243s 


.921 16 


1.08559 


.95395 


1.04827 


.98786 


1.01229 


21 


40 


.85912 


1.16398 


.88992 


x.i 2369 


.92170 


1.08496 


.95451 


1.04766 


.98843 


1. 01 170 


20 


41 


.85963 


1.16329 


.89045 


I. I 2303 


.92224 


1.08432 


.95506 


1.04705 


.98901 


I.0III2 


19 


42 


.86014 


1.16261 


.89097, 


1.12238 


.92277 


1.08369 


.95562 


1.04644 


.08958 


1. 01053 


18 


43 


.86064 


1.16192 


.89149 


1.12172 


.92331 


1.08306 


.95618 


1.04583 


.99016 


I.00994 


17 


44 


.86115 


1.16124 


.89201 


1.12106 


.92385 


1.08243 


.95673 


1.04522 


.99073 


I.00935 


16 


45 


.86166 


1. 16056 


.89253 


1.12041 


.92439 


1.08179 


•95729 


1. 0446 1 


.09131 


I.O0876 


15 


46 


.86216 


1.15087 


.89306 


1.11975 


.92493 


1.08116 


.95785 


1. 04401 


.99189 


1. 008l8 


14 


47 


.86267 


1.15919 


.89358 


I. 11909 


.92547 


1.08053 


.95841 


1.04340 


.99247 


1.00759 


13 


48 


.86318 


1.15851 


.89410 


1. 1 1844 


.92601 


1.07990 


.95897 


1.04279 


.99304 


1. 00701 


12 


49 


.86368 


1.15783 


.89463 


1.11778 


.92655 


1.07927 


■95952 


1. 04218 


.99362 


I. OO642 


II 


50 


.86419 


1.15715 


.89515 


1.11713 


.92709 


1.07864 


.96008 


1. 04 1 58 


.99420 


1.00583 


10 


51 


.86470 


1.15647 


.89567 


1.11648 


.92763 


1. 0780 1 


.96064 


1.04097 


.99478 


1.00525 


§ 


52 


.86521 


1.15579 


.89620 


1.1x582 


.92817 


1.07738 


.96120 


1 .04036 


.99536 


I.OO467 


53 


.86572 


x.i55» 


.89672 


1.11517 


.92872 


1.07676 


.96176 


x. 03976 


.99594 


1.00408 


7 


54 


.86623 


1. 15443 


.89725 


I. 11452 


.92926 


1. 076 1 3 


.96232 


1-03915 


.99652 


1.00,350 


6 


55 


.86674 


I.I5375 


.89777 


1.11387 


.92980 


1.07550 


.96288 


1.03855 


.99710 


1. 00291 


5 


56 


.86725 


x. 15308 


.89830 


1.11321 


.93034 


1.07487 


.96344 


1.03794 


.99768 


1.00233 


4 


3 


.86776 


1. 1 5240 


.89883 


I.I 1256 


.93088 


1.07425 


.96400 


1.03734 


.99826 


I.OOI75 


3 


.86827 


1. 15172 


.89935 


1.11191 


.93143 


1.07362 


.96457 


1.03674 


.99884 


I .O0Il6 


2 


59 


.86878 


1.15104 


.89988 


1.11126 


.93197 


1.07299 


.96513 


1. 036 1 3 


.99042 


I.OOO58 


I 


60 


.86929 


1. 15037 


.90040 


1.11061 


.93252 


1.07237 


.96569 


1.03553 


1. 00000 


I. OO0O0 





/ 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


Cotang 


Tang 


/ 


4< 


)° 


41 


s° 


4; 


7° 


4< 


3° 


4. 


5° 



Table of Angles for 
Gashing Worm Wheels 



n8 



BROWN & SHARPE MFG. CO. 



tfX 

W 

w 
a 

p* 
o 

o 

55 

Q 

< 

o 

o 
fa 

to 
W 
i4 
O 

< 
fa 

o 
fa 

i-T 

<! 



1 


~l» 


































1 


H« 


































1 


w|» 


































1 


«l« 


































1 


- 


































s i 


dr 
































°iO 


*! 


"if 




























"eo 


"^> 




"I 


•3T 
























"eo 
O 


"cm 


"eo 




•o 


1 


e«|» 


















"e* 

so 


"•* 


*3» 
O3 


3 K» 


"oo 


c 4. 


cp 
eo 


s 


6 3 


1* 
















°eo 


3 o 




°iO 






St 




o 
""•ft 


1 


ex 












*•« 










»« 


"eo 

eo 
o ■ 


"r- 


"eo 


1? 


"e» 

ep 

"eo 


'3 


* 








"eo 

°ao 


O 






"eo 

3 iO 




so 


"2 


"eo 


°eo 


"« 

eo 

c eo 


3 

c co 


°eo 


-*< 


ex 




^2 

°2 


00 






°co 


a 2 




"00 
0^, 






°eo 


o 
°eo 


c c4 


1— 

°2 


°co 


1 


# 


CO 


1§ 

3 e» 


°00 






"o> 


''iO 


■a 




"o 

°2 


°to 


J? 




C S 


°co 


*3 

°ex 


1 


* 


"e» 

© 


°e» 






"li 


*5 




o7 


V* 


^3 


°eo 


J9 

°eo 


3 

°eo 




3 


It 

°00 


1 


•sir 


■ft 

o > 
© 


■f 
°ae 


O 1 

t— 


"«o 

CO 








^ 

°-«i« 




°eo 


eo 
°eo 


2 

°eo 


°eo 




°ci 


CO 


1 


» 




"eo 

3 ao 


> 


"eo 


~9 






"eo 

°4. 


°eo 


°eo 


°eo 


°co 




ex 
°2 


eo 

eo 

°c>» 


a 

°cx 


1 


•*• 


°s 


3 






f 


"o 


<* 


"30 
CM 

"eo 


ex 

°eo 




"i<- 

C4 






"e» 


"ex 

°ex 


"<» 

°ex 


1 


■* 


"<© 

1 


°eo 


"ex 


7 


"eo 


°eo 




"e>» 

"eo 


"oo 

•*• 


"i» 

eo 


CO 
<N 


"l— 






3 


"e» 


1 


■*■ 




'eo 

ex 

°H9 


eo 




"«P 

eo 
°eo 










"o» 


o 


°e>* 


S 


"oo 


51 


I? 


1 


•o 


"e» 




"© 

<** 


°eo 


"3 


> 


"o» 

CO 

°N 






"n9 


o? 


It 


"eo 






R 


=00 


* 


"oo 




•5 


"en 

o ■ 


> 






"eo 




o? 


oT 


"» 

so 


o? 


? 


o3 


'8 


1 


«o 






09 


"fit 

P SO 






"eo 






""♦ 


o eo 


oo 


o? 


S5 


5 


CO 


-8 


-A" 


If 


"5 
C CO 


~CX 

c CO 


"00 

°ex 


«o 


~J3 






-* 


o? 


o? 


o? 


"■» 


"H9 


'3 


"t— 




- 




"8 

c eo 


°cx 


~co 

CO 

c ex 




o? 

*» 


o? 


o? 


eo 


o? 


"S 


"oo 


"s 


"as 


"» 

C li 


"eo 


"eo 

s 


Tf 


°0» 


°eo 


ex 


C ex 


"o 


K 


"s© 


CO 

o ' 


o? 


a 


09 


"eo 


"e» 


"k» 


I? 


g 


1 


00 


3 

°C9 


"ex 

°eo 




°ex 


"Cjl 


c? 


? 


eo 


o? 


"oo 


eo 

o I 


"oo 


«2 


°i 


-g 


S 


2 


en 


"3 
r CO 


"ex 

°CX 


"en 

e ex 


"f* 

C eX 


"00 


o? 


«# 


s* 


"i« 


"o» 


"•O 


5 


"is 


s 


O 


"e» 


1 


o 


"8 

°e* 


IS 
°ex 


°ex 


Si 


o? 


o? 


o? 


2 


r— 


"e>» 


s 


a 


ss 


"o» 


"eo 


5 


Q 


I 
</> o 

Q. 


«c|ao 


«+• 


H« 


- 


Hf 


dr 


H» 


-Jr 


■i* 


l* 


H«, 


C4 




CM 


csloo 

C-l 


ex 












si 


d3i 


3WV 


IQ H 


Oil 


d 






• 







BROWN & SHARPE MFG. CO. 



II 9 



1 

T 

wi 

►4 
W 
W 

w 

o 

o 

a 

in 
<! 
O 

O 
to 

en 

to 
h4 
O 

<1 

to 
O 

to 
■-J 

pq 

<! 
in 



1 


~l» 
















"8 

■a 


'1 




c5 


1 


r 

°2 


•S 


OS 


> 

°OS 


1 


J|« 














J 


"09. 




"0j» 

°co 


"8 
01 


0? 


so 


"so 

°«o 


"'OS 

"so 


"09 

°co 


1 


«|« 








"o9 
°OS 


?5 




"JO 

5 


3 




°A 


3 


Sm 


K9 


? 
°-i" 


3 


> 

«* 




«|* 








4J 


=? 






3 » 


"CM 






3 4« 




"8 


"09 


"cm 


§ 


- 


"3 




"os 
°«o 


"09 


"8 






"0 

eo 


V- 


"09 


? 


g 
% 


°09 


"OS 
°09 


"0 

°C9 


°09 


8 


~Jr 




"V- 




•0 


3 L 


*o 




"OS 

09 


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15 


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09 


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•sy3i3wvia HOiid 



BROWN & SHARPE MFG. CO. 121 



TABIJES OF PRIME NUMBERS AND FACTORS. 

In making use of these tables, the following explanation 
may be of assistance : the two columns at the left give the 
last two figures of the number to be factored ; the first 
column gives all numbers to 50 and the second column from 
50 to 100. 

Example i. — Required, the factors of 138. Refer to 
the column of numbers from 100 to 150 and follow down 
the column until opposite 38 in the left-hand column; the 
factors are found to be 2 X 3 X 23. 

Example 2. — Required, the factors for 1672. Refer to 
the column of numbers from 1650 to 1700 and follow down 
the column until opposite 72 in the second column at the 
left ; the factors are found to be 2 3 X 1 1 X 19 or, more con- 
veniently stated for factoring, 2X2X2X11X19. 



123 BROWN A SHARPS MFG. CO. 

PRIME NUMBERS AND FACTORS 1-10200. 



From 
To 



o 
50 



50 
zoo 



zoo 

150 



Z50 

200 



200 
250 



250 
300 



o 

z 

2 

3 

4 



9 
zo 

zz 
12 
13 
14 
15 
16 

17 
18 

19 
20 

2Z 
22 
23 
24 
25 
26 

27 
28 

29 
30 

31 
32 
33 
34 
35 
36 

3 Z 
38 

39 
40 

41 
42 
43 
44 

a 
n 

49 
Li2_ 



50 
5i 
5« 
53 
54 
55 
56 

5 l 
58 

59 
60 

61 
62 
63 

2 4 
65 

66 

67 

68 

69 

70 

7i 
72 

73 
74 

76 
77 
78 
79 
80 

81 
82 
83 

2 4 
85 

86 

87 
88 

89 
90 

9i 
92 
93 
94 
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96 

9 l 
98 

99 

100 



2-3 



2-5 



2''3 



2.7 

3-5 
2* 



2-3' 

ii" s " 

3-7 

2-II 



2-3-5 



2* 

3'" 

2.17 



2.19 

3 3 13 

2 3 -5 



2-3-7 



2** 1 1 

3 a -5 
2.23 



2 4 -3 

7 2 
2-5 2 



2-5* 
3-'7 



2-3* 

2 J -7 
3-!9 
2*29 



2 2 -3'5 



2.31 

5-13 
2.3.II 



2M7 
3-23 

2-5-7 



2 J -3 a 



2 3 -3 


2-37 

3'5 2 


5* 


2 ; 13 


2 2 -I9 


3 


7.11 


2«. 7 


2-3-13 



2 4 -5 

3 4 
2.41 



2 2 -3-7 
5-i7 
2-43 
3-29 

2 8 «II 



2-3 a -5 
7-i3 

2 2 -23 

3-3 1 ' 
2.47 

5-»9 
2 6 -3 



2-7 a 

2*-5* 



2 t. 5 i 



2.3.17 



2 3 -i3 
3-5-7 
2-53 



2 2. 3 3 

2-5-u 

3*37 
2 4 -7 



2.3.19 

2 2 -29 

3 2 'i3 
2-59 
7.17 

2 3 -3-5 



2-6l 

3-41 
2 j" 31 



2 7 

3-43 
2-5-13 



3-47 
2.71 
ii« 13 

2 4. 3 2 

5-29 

3-7 1 

2 2 -37 



•3-5 f 



2 3 «I9 

3 2 -^7 
2. 7. 11 

5;3* 
2*-3' I 3 



2-79 
3-53 
2 6 -5 

2-3* 



2*.4I 

3*5-" 
2.83 



28.3.7 

i3 a 
2-5*17 

3*' 1 9 
2" 2 -43 



2-3-29 

5 2 -7 

2 4 -II 

3*59 
2-89 



2*-3-n 

7.19 

2-67 
3 3 '5 

2 8 -l7 

2-3-23 

2 2 -5'7 



2 2 -3 8 -5 



2-7-13 
3.61 

2 3 '23 

5-37 

2-3-31 

11-17 

2 2 -47 

3 3 '7 

2.5.19 



2«. 3 



2-97 

3-5-13 

2*.7« 



2-3 2 .II 



2 3. 5 2 

3-67 
2-IOI 
7.29 
22.3.17 

5-41 
2-103 

3 2 -23 

2*. 13 
11-19 
2-3-5-7 



2 2 -53 

3-7i 

2-107 

5*43 

2 3. 3 3 

7-3i 
2-109 

3*73 
22.5.11 

13-J7 
2-3-37 



2'-7 

3 2 -5 a 
2-113 



22.3.19 

2-5-23 

3-7-n 

2 3 «29 



2-3 2 -i3 

5-47 

2 2 -59 

3-79 

2-7.17 

2 4 -3'5 



2-3-5* 



2-''5 a 



2-II 2 

3 5 
2 2 -6i 

5'7 2 
2.3.41 

I3-I9 

2 3 '1I 

3-83 

2-5 3 



2-5 s 
2 2 -3 2 '-V 

11.23 

2-127 
3-5-17 

2 8 

2 -3-43 

7-37 

2 2 -5-i3 

3 2 - 2 9 
2-131 

23.3.11 

5-53 
2.7.19 

3-39 
22.67 

2-3 3 -5 



2M7 
3-7-J3 

2-137 
52.11 

2 2 -3-23 



2-139 

3 2 \$i 
2 8 -5-7 



2-3-47 



22.71 

3-5-19 

2. 11. 13 

7.41 

2^-3 2 

i7 2 

2.5.29 

3-97 
2 2 -73 

2-3-7 2 

5-59 

2 3 -37 

3«.u 

2.149 

13-23 

2 2 -3-5 2 



BROWN & SHARPE MFG. CO. 



123 



From 
To 



300 
350 



350 
400 



400 
450 



450 
500 



500 
550 



550 
600 



o 

z 

2 
3 
4 
5 
6 

7 
8 

9 
zo 

zz 
za 
13 
14 
15 
16 

17 

18 

19 
20 

21 
22 
«3 
24 
25 
26 

27 
28 
29 
30 

3i 
3* 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 
43 
44 
45 
46 
47 
48 

49 

lioj 



50 
51 
5* 

53 
54 

11 

6l 
62 

2 3 

I* 
65 

66 
67 
68 
69 
70 

7i 

72 

73 
74 
75 
76 

77 
78 

I 9 
80 

81 
82 

84 
85 
86 

87 
88 

89 
90 

91 
92 
93 
94 

96 
97 
98 

99 
zoo 



2 2 -3'5 2 
7-43 
2-151 
3.101 

2 4 » 19 

5'6i 
2.32.17 

2 2 «7.II 

3-103 

2-5-3 1 



2 3. 3 . I3 

2-157 

3 2 -5-7 
22.79 



2-3-53 
11.29 
26.5 

3.107 

2.7.23 

17.19 

2 2 -3 4 

5 2 -i3 

2.163 

3.109 

2 3 «4I 

7*47 
2-3-5-" 



22.83 

3 2 -37 
2-167 

5-67 
2^.3.7 

2-i3 2 

3- 1 13 

22.5.17 

11-31 

2.32.19 

7 3 

2 3 -43 

3-5-23 

2-173 



2.52.7 
3 3 -!3 

2 5 »II 



2 4. 5 2 



2-3-59 

22.89 

3-7-17 
2.179 



2 3 -3 2 '5 

2-l8l 

3-n 2 

22.7.13 

5-73 
2.3.61 



2 4 -23 

3 2 '4i 
2-5-37 

7-53 
2 2 -3*3i 

2. 11-17 

3'5 3 ' 

2 3 -47 

13-29 
2.33.7 

22.5.19 

3- I2 7 
2-191 



2 7 -3 

5-7-n 

2-193 

3 2 -43 

2 2. 97 



2-3-5-13 
17-23 

2 3. 7 2 

3-I3I 
2.197 

5-79 
22.32.11 



2-3-67 
i3-3i 

2 2 «IOI 

3 4 '5 
2.7-29 

"•37 
23.3.17 



2.5.41 

3-137 
22.103 

7-59 

2-3 2 -23 

5-83 

2 5 -i3 

3-139 

2. ii. 19 

2 2 -3'5-7 



2. 211 
3 2 '47 
2 3 -53 
5 2 -i7 
2-3-71 
7.61 

2 2 -I07 

2-5-43 



2 4. 3 3 



2.7.31 
3-5-29 

2 2 - IO9 

19-23 

2-3-73 



22.3.29 

2-5 2 '-'7" 



2.199 
3-7-19 

2*. 5 2 



2 d .5.II 

3 2 -7 2 
2-13-17 

2 2 -3-37 

5-89 

2-223 

3- H9 

2 6 «7 



2-3 2 -5 2 

11-41 

22.113 

3-i5i 
2-227 

5-7-13 
23.3.19 

2*229 
3 3>I 7 
2 2 -5-23 



2.3.7.11 

2 4 '29 
3-5-31 

2-233 
2 2 -3 2 -i3 

7.67 

2-5-47 

3-157 
2 3. 59 

n-43 
2-3-79 
5 2 -i9 
22.7.17 

3 2 -53 
2-239 

2 5 -3-5 

13-37 
2-241 

3-7*23 
22.112 

5-97 
2-3 5 

2 3 -6l 

3-163 

2.5.72 



22.3.41 

17.29 

2-13-19 

3 2 -5-n 

2 4 -3i 

7.71 

2-3-33 



2*-5* 

3.167. 
2.251 



23.32.7 

5«ioi 
2.11-23 

3-M 2 
22.127 

2-3-5-17 
7-73 

2* 
3 3. I9 

2-257 

5-103 

2 2 -3*43 
11.47 

2-7-37 
3- J 73 
2 3 -5-i3 



2.32.29 

22.131 

3*5 2 -7 
2-263 

I7-3 1 

2 4 -3-II 

2 3 2 
2-5-53 

3 2 '59 
22.7.19 

I3-4I 
2-3-89 
5.107 
23.67 

3*!79 
2.269 
72.11 

2 2 -3 3 -5 



^isl 



2-271 
3.181 

2 5 »I7 

5.109 
2-3-7-13 



22.137 
32.61 



2-5 z -ii 

19.29 

2 3 -3-23 
7-79 

2.277 

3-5-37 
22.139 

2-3 2 -3i 

13-43 

2 4 -5-7 

3.11.17 

2-281 

2 2 -3'47 

5*"3 

2.283 

3 4 -7 
23.71 

2-3-5-19 



11 



22.11.13 

3 !l 9i 

2-7-41 

5 2 -23 
26.32 



2.17 2 

3 !l 93 
22.5.29 

7-83 

2-3*97 

"•53 

2 8 -73 

3 2 -5-i3 

2-293 

22.3.7V 

J9-3 1 
2-5-59 

3-197 

2 4 -37 

2-3 3 .II 

5-7-17 

2 2 «I^9 

3^99 
2.13.23 

2 3 -3-5 2 



I2 4 



BROWN & SHARPE MFG. CO. 



From 
To 



o 

X 
2 

3 

4 
5 
6 

7 
8 

9 
zo 

XI 
12 

13 
14 

16 

17 
18 

19 
20 

2X 
22 
*3 

«4 
*5 
26 

11 

29 

30 
31 

3« 
33 
34 
35 
36 

38 
39 
40 

4i 
42 
43 
44 
45 
46 
47 
48 
49 
5Q 



50 
5i 
5* 
53 
54 

56 
57 
58 

60 

61 
62 
63 

65 
66 

u 

69 
70 

71 

72 

73 
74 
75 
76 

;i 

79 
80 

81 
82 
83 
84 

Si 

87 

88 
89 
90 

9i 
92 

93 
94 

96 

97 
98 

99 
100 



600 
650 



2 8 -3-5 2 



2-7-43 
32.67 
22.151 

5-n 2 
2.3.101 

2 5 »I9 

3-7-29 
2.5.61 

13-47 
2^.32.17 

2.307 

3-5-41 
23.7.11 

2-3-103 

2^.5-31' 

3 8 '23 
2-311 
7.89 

5*' 

2-3I3 

3-H-I9 
22.157 

17-37 
2-3 2 '5-7 



2 8 -79 
3-2M 
2-3I7 

5-127 

2 2 -3*53 
7 a 'i3 
2. 11. 29 

3 2 -7i 
2 7 -5 



2.3.107 

22.V-23 

3-5-43 
2.17.19 

23.34" " 

"•59 
2'5 a -i3 



650 
700 



2-5 2 -i3 

3-7-31 

22.163 

2.3.109 
5-I3I 

2 4 »4I 

3 2 -73 

2.7.47 



22.3.5.11 



2-331 

3-I3-I7 

2 3 -8 3 

5-7-19 
2-3 2 -37 
23-29 
22.167 

3-223 
2.5.67 

ii«6i 
2 5 -3-7 

2-337 

3 3 -5 2 
22.132 



2-3-H3 

7-97 

23.5.17 

3-227 
2.11.31 



22.32.19 

5-137 
2.73 

3-229 
2 4 -43 
13-53 
2-3-5-23 



22.173 

32.7.11 

2-347 

5-139 

23.3.29 

17.41 

2-349 

3-233 

2 2 -5 2 -7 



700 
750 



22.52.7 



2.33.13 
19-37 

2«.II 

3-5-47 
2-353 
7.101 

2 2 -3-59 



2-5-71 

3 2 -79 

2^.89 

23-3I 
2.3.7.17 

5-H-I3 
22.179 

3-239 
2-359 



2 4 -3 2 -5 

7.103 
2-192 

3-24 1 
22.181 

5 2 -29 
2-3-n 2 



23.7.13 

3 6 

2-5-73 

17-43 
22.3.61 



2.367 
3-5-7 2 

2 6 -23 
II.67 
2.32.41 

2 2 -5-37 

3-I3-19 
2-7-53 

2 3 -3-3i 

5-H9 

2-373 

3 2 -»3 

22.11.17 

7.107 
2-.V5 3 



750 
800 



2-3-5 5 



2 4 -47 

3-251 

2-13-29 

5-i5i 

2 2 -3 3 -7 

2-379 

3-H-23 

2 3 -5-i9 



2.3.127 
7.109 

2 4 -I9I 

3 2 '5-i7 
2-383 
13-59 
2 8 -3 



2-5-7-n • 

3-257 
22.193 

2-3 2 -43 

5 2 '3i 
2 3. 97 

3-7-37 
2-389 
19.41 

2 2 -3-5-i3 

11. 71 
2-17-23 

3 3 *29 
2**72 

5-157 
2-3-131 

22.197 

3-263 

2-5-79 

7-ii3 

2 a .3 2 -II 

13-61 

2-397 

3-5-53 
22.199 

2.3.7.19 

17-47 

2»-5 2 



800 
85O 



:% 



2 5. 5 

3 2 - 

2.401 

n-73 
22.3.67 

5-7*23 

2-13-31 

3.269 

2 3 «IOI 



2-3 4 -5 



22.7.29 

3-271 

2-H-37 

5-163 

24.3.17 

19-43 
2.409 

3 2 -7-i3 
22.5.41 



2-3-137 

2 3 • 103 
3-5 2 -ii 
2-7*59 



2 2 -3 2 -23 

2-5-83" 

3-277 
26.13 

7 2 'i7 
2-3-139 
5.167 
22.11. 19 

3 3 -3i 
2.419 

2 3 -3'5-7 

29* 

2*421 

3.2S1 

2 2 .2II 

5-i3 2 

2-3 2 -47 
7. ii 2 

2 4 -53 
3-283 
2-5 2 »i7 



850 
900 



2.52.17 

23*37 
22.3.71 

2.7.61 
3 2 '5-i9 

2 3 -I07 

2-3-11-13 

2 2 -5-43 

3-7-41 
2-431 

2*. 3 «"" 

5-173 
2-433 
3-i7 2 
22.7.31 

"•79 
2-3-5-29 

13.67 

2 3 «I09 

3 2 -97 
2-19-23 
5 3 -7 
2 2 -3'73 



2-439 
3-293 
24.5.11 



2.32.72 

22.13.17 

3-5-59 

2-443 



2*-3'37 

7- 

2. 



7.127 
2-5-89 



3M1 

2 2 -223 

I9.47 

2.3.I49 

5-179 

2'. 7 

3-I3-23 

2-449 
29.31 

22 - 3 2 -5 2 



J 



BROWN ft SHARPE MFG. CO. 



"5 



From 
To 



900 
950 



950 
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128 



BROWN A SHARPE MFG. CO. 



From 
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1800 
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1900 



1900 
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2.52.41 

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2.5.11.19 

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2 2 -523 

7-13-23 

2-3-349 

5-4^9 
24.131 

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2 2 - 3-5 2; 7' 



BROWN A SHARPE MFG. CO. 



129 



From 
To 



azoo 
2150 



2150 
aaoo 



aaoo 
2250 



2250 
2300 



2300 
2350 



2350 
2400 



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1 
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2-31-37 
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2 3 -l7 2 

3 2 -257 
2.13.89 

5-463 
2 2 -3-i93 
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2-3 3 '43 
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22.7.83 

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2*1163 

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17-I37 
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2 -7-37 
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2-5 2 -47 

13.181 

2*11*107 

3-5-157 
22.19.31 

2*32*131 

7-337 

2 3 -5-59 

3-787 
2.1181 

17-I39 
22.3.197 

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2.7.13 2 

3 2 -263 
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2 2 -593 
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2-5-239 

3-797 
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2-3 2 -7-i9 
5-479 
2 -599 
3-17-47 
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2 5 -3-5 8 



13° 



BROWN & SHARPE MFG. CO. 



From 
To 



2400 
«450 



«450 
2500 



2500 
3550 



«550 
2600 



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2650 
2700 



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22.32.67 

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22.5.11* 

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3.829 

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2 2 -5 4 
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2^3.211 
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2 4 -3-53 

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3 2 -28 3 

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2-3-5 2 -^7 

2 3 .II.29 

3-23-37 

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2-1279 
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2.3^.61 

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3 3 '5-i9 

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2-5-257 

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2.32. 11. 13 

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2 2 -3-5-43 

29.89 
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23.17.19 

5- "-47 
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22.647 

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2 5. 3 4 



2-1297 

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2 3 -5 2 -i3 



28.52. 13 

3 2. I7 2 

2.I30I 

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2 4 -i6 3 



2.32.5.29 

7-373 
2 2 -653 

3-I3-67 
2-1307 
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23.3.109 

2-7. 11. 17 

3 3 -97 

22.5-131 



2.3.19.23 
43.61 

2 6 »4I 

3'5 3 -7 
2.13.101 

37-7i 
2 2 -3 2 -73 
11.239 
2.5.263 

3-877 

23.7.47 

2-3-439 
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22.659 

3 2 '293 
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2 4 -3-5-" 

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2.1321 
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22.661 

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2.33.72 

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2-5 2 -53 



2-5'-53 
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7-379 

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5-I3-4I 
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2M67 

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2.7.191 

52.107 

22.3.223 

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28.5.67 

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22.11.61 

3-5-179 
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2-5-269 

3 2 -i3-23 
22.673 

2-3-449 
5.72. 11 

2 3 -337 
3-29-3I 
2. 19.71 

2 2 -3 3 -5 2 



BROWN & SHARPE MFG. CO. 



*3i 



From 
To 



2700 
2750 



2750 
2800 



2800 
2850 



2850 
2900 



2900 
2950 



2950 
3000 



o 

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2»-3*-5* 

37-73 

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28.3.H3 

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22.7.97 

11. 13.19 

2.32.151 

25.5.17 

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2.1361 

7-389 

22.3-227 

52.109 

2.29.47 

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2 3 .II«3I 

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22-683 

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2.1367 

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7.17.23 

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3-11-83 

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11*251 

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2 4. 5 2. 7 



2.3.52.19 



2-3-463 

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2-3-457 
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2.3.467 



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2.3. 1 1.43 
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22.23.31 

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2-3 3 '53 

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2.7-11.19 

2 4 .3«6i 
29.101 
2-5-293 

3-977 
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7.419 
2.32.163 

5-587 
23.367 
3. 1 1.89 
2.13.113 

2 2 -3-5-7 2 

I7-I73 
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33.109 

2 7 -23 

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22-11.67 
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2-5 2 -59 
13.227 

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2-7. 211 
3-5-197 
2 2 -739 

2.3.17.29 
11-269 

2 4 -5-37 

3 2 -7-47 
2.1481 

22.3.13.19 

5-593 
2.1483 

3-23-43 

2 3 -7'53 

2.33.5.1] 



2^-743 

3-991 

2.1487 

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2 3 -373 

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3-997 

2 4 «II-I7 

4 J -73 
2-3-499 
5*599 
22.7.107 

3 4 -37 
2.1499 

2 3 -3-5 3 



132 



BROWN A SHARPE MFG. CO. 



From 
To 



3000 
3050 



3050 
3100 



3200 
3150 



3150 
3200 



3200 
3*50 



3350 
3300 



o 

z 

2 

3 

4 



7 
8 

9 
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11 
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38 

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43 
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50 
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61 
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81 
82 
83 
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87 
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2.17.89 
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2 3 -379 

3 2 -337 

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2-3 2 -i3 a 

17.179 

22.761 

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22.769 

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25.5.7.11 

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2.3.877 

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3-7-251 
23.659 



2.32.293 

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22.32.11.13 
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3-1747 

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72.107 

22.3.19.23 

5.1049 

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29.181 
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2. 19.139 

3 2 '587 
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2.11*241 

23.3.13.17 
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2-7-379 
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3.7.11.23 

2.2657 

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3-5 2 -7i 

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23.23.29 

3 2 -593 

2-17-157 

19.281 

22.3.5.89 

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2.2671 

3-I3-I37 
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2.52.107 



2.3.883 

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22.7.191 

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28.3.223 

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3 2 '599 
2 4 -337 

2.3.29.31 

5-I3-83 
22.19.71 

3-7-257 
2.2699 



3 -3 3 -5 2 



140 



BROWN & SHARPE MFG. CO. 



From 
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22.13.107 

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2-5-557 

32.619 
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2.3.929 

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2.2791 
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2 s -3' 2 33 
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2 5 -5 2 -7 
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5-19-59 
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22.1409 

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2.7.13.31 
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2.52. 113 
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5.17.67 

2 6 -89 

33.211 

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2 2 -3-5 2 -i9l 



BROWN & SHARPE MFG. CO. 



141 



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142 



BROWN & SHARPE MFG. CO. 



From 
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6000 
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6050 
6100 



6100 
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BROWN & SHARPE MFG. CO. 



M3 



From 
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2-3.1087 

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2-52.131 

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BROWN & SHARPE MFG. CO. 



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23.3.283 

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BROWN & SHARPE MFG. CO. 



HS 



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2 s -3'5-59 

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146 



BROWN A SHARPE MFG. CO. 



From 
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7200 
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23-3I7 

22-1823 
3.11. 13.17 
2-7.521 

5* H59 
2^.3.19 



2 4 -3-i5i 
11.659 

2-5 3 -29 



2.41.89 

32.811 

22 '5 2 -73 



2. 19. 193 

3 2 -5-i6 3 

23.7.131 

11.23.29 

2.3.1223 

41.179 

22.5.367 

3*2447 
2.3671 
7.1049 
24.33.17 

5-i3-ii3 

2-3673 

3-31-79 

2 2 . II. 167 

2-3-5 2 -7 2 



2.3.52.72 

23.919 

3 2 - 19-43 
2.3677 

5-i47i 

22.3.613 

7-1051 

2-13-283 

3.11.223 

2 6 -5-23 

17-433 
2.32.409 

37-199 
22.7.263 

3-5-491 
2-29.127 

53-^39 
23.3.307 

2.5.11-67 

3 4 -7-i3 
22.19.97 

73.101 

2-3.1229 

5 3 -59 
24.461 

3-2459 
2-7-I7-3I 

47-157 

2 2. 3 2. 5 . 4I 

II 2 .6l 

2-3691 

3.23.IO7 

23.i3.7i 

5.7.2II 

2-3-I23I 

83-89 

22-1847 

3 2 -82i 

2-5-739 

19.389 
2S.3.7.11 

2-3697 

3-5-I7-29 
22.432 

13-569 
2 i 3 8 -i37 

72.151 



2 8 -5 2 '37 

3-2467 

2.3701 

11.673 

22.3.617 

5.1481 

2.7.232 

3 2 '823 
2 4. 4 6 3 

3I-239 
2-3-5-i3' I 9 



22.17.109 

3*7-353 

2-H-337 

5-1483 

2 3 «3 2 -io3 

2-3709 
3-2473 
2 2 -5-7-53 

41*181 

2.3.1237 

i3-57i 

2 8 «29 

3 8 '5 2 '" 
2.47.79 

7.1061 
2 2 «3«6i9 
17.19.23 
2-5-743 

3*2477 
23.929 

2-3 2 '7-59 

5-1487 
2 2 . 11. 132 

3-37-67 
2-37I9 
43-173 
2 4 -3*5-3i 

7-1063 
2.61 2 
3 2 -827 
22.1861 

5-1489 

2-3' I 7-73 

11.677 

23.72.19 

3 : i3'i9i 

2 '5 2tI 49 



2.52.149 

22.34.23 

29-257 
2-3727 
3-5-7-71 
25.233 

2-3-11-113 

2 2 -5-373 

32.829 
2-7-13-41 

1 7-439 
23.3.3H 

5- H93 
2-3733 

2 2 -i867 
7. 1 1.97 
2-3 2 -5-83 

31.241 
24.467 

3-47-53 
2.37. 101 

5 2 'i3-23 



13-23 
3.7.89 



2-3739 
33.277 

28.5.11.17 



2-3-29-43 

7.1069 

2 2 -i87i 

3-5-499 
2.19.197 

26.32.13 

2-5.7-107 

3.11.227 
22.1873 
59-127 
2.3.1249 

5- H99 
2 3. 937 
3 2. 7 2. I7 

2.23.163 



BROWN & SHARPE MFG. CO. 



M7 



From 
To 



7500 
7550 



7550 
7600 



7600 
7650 



7650 
7700 



7700 
7750 



7750 
7800 



o 

z 

2 

3 

4 

i 

7 
8 

9 
10 

11 
12 
13 
14 

16 

17 
18 

19 
20 

21 
22 
«3 

24 
25 
26 



29 
30 

31 

3* 
33 
34 

36 

38 
39 

40 

41 

4* 
43 
44 
45 
46 

47 
48 
49 
39. 



50 
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5« 
53 
54 
55 
56 
57 
58 

60 

61 
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69 

70 

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72 

73 
74 
75 
76 

77 
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81 
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83 
84 
85 
86 

87 
88 

89 
90 

91 
92 
93 

94 
95 
96 

97 

98 

99 

100 



2 2 -3'5 4 
13*577 
2. 112.31 
3.41.61 
2*. 7.67 
5.19.79 

2-3 8 'i39 

22.1877 

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7.29.37 

2 3 -3-3 x 3 
11.683 
2.13.17 s 
32.5.167 

2 2 . 1879 

2.3.7.I79 
73-I03 

2 5 -5-47 

3.23.109 
2.3761 



2.52.151 

3 2 -839 

2 7 -59 

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2.3.1259 

5-1511 

22.1889 

3.11.229 

2-3779 

33.33.5.7 



2.19.199 

3-2521 

22.31-61 

5.17.89 

2-3' I 3-97 

7-23-47 

2 4 -n-43 
32.292 

2-5-757 

67.113 
2 2 -3-63i 



2 2 «3 2 .ii.i9 

5 2 -7-43 

2-53-71 

3- x 3-i93 

2 3 '94i 

2-3-5-251 

17-443 
22.7.269 

3 5 '3i 
2.3767 

5-"-i37 
2 4 -3-i57 

2.3769 

3-7-359 
22.5.13.29 



2-7-54 1 
3.52. 101 
23.947 

2.32.421 
"•13-53 
2 2 -5-379 

3-7-I9 2 
2.17.223 

25.3.79 

5-37-4 1 
2-3793 
33.281 
22.7.271 



2 4 -5 2 -i9 

11-691 

2.3.7.181 



22.1901 

3 2 -5-i3 a 
2.3803 

2 8 -3-3i7 
7.1087 

2-5-761 

3-43-59 
22. 11. 173 

23-331 

2-3 4 '47 

5-1523 
2«. 7 .i 7 

3-2539 
2-13-293 
19.401 
22.3.5-127 



2-37.103 
32.7.U2 

2 3 -953 

58.61 

2.3.31.41 

29.263 

22.1907 

3-2543 
2.5.7.109 

I3-587 

2 4 -3 2 '53 
17.449 

2. 1 1.347 

3-5-509 
22.23.83 
7.1091 
2.3.19.67 



.17 



2-3-5-"-23 



2.32.419 

19-397 
28.23.41 

3-5-503 
2-73. 11 

22.3a7.37 
2-5 2 -i5i 



23.13.73 

3-2531 

2-3797 

5-7 2 -3i 
22.32.211 

71.107 

2.29.131 

3.17.149 

2 4 >5 2 -i9 



23.5.191 

3 s -283 

2.3821 

22.3.72. I3 

5-H-I39 
2.3823 

3-2549 
25.239 



2-3 2 -5 s 
7^093 
22.1913 

3-2551 
2.43.89 

5-I53I 
28.3.11.29 

I3-I9-3I 
2-7-547 
3 2 - 2 3-37 
2 2 -5-383 

47-163 

2.3.1277 

79.97 

2 4 -479 
3-5-7-73 
2-3833 
11. 17.41 
22.38.71 

2-5-13-59 

3-2557 
28.7.137 



22.52.7.!! 

3-i7-i5i 
2-3851 



2-5 a -3i 
23-337 
23.3.17.19 



2.3.1279 

5 2 -3°7 
22.19.101 

3 2 -853 

2-H-349 

7.1097 

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2.23.167 

3 Bl 3'i97 
22.17. 113 

5-29-53 
2.32.7.61 

28.312 

3-H-233 
2.5.769 



22.3.641 

7 2 -*57 
2.3847 

3 4 -5-i9 
2 4 -i3-37 
43' 1 79 ft 
2.3.1283 



28.32.107 

5-23-67 

2-3853 

3-7-367 

22.41.47 

13-593 
2-3-5-257 

1 1« 701 
25.241 

3 2 '857 
2*7.19.29 

5-1543 
22.3.643 

2.17.227 

3-3 J -83 
28.5.193 

7. 1 103 
2-38. 11. 13 



2^.1931 

3-5 2 -io3 

2-3863 

2 4 -3-7-23 

59-i3i 

2-5-773 

3 2 '859 
22.1933 

11. 19.37 
2.3-1289 

5-7-I3-I7 
28.967 

3-2579 
2-53-73 
71.109 

2 2 -3 2 *5-43 



2-3 2 -5 2 -i7 



22.52.7.11 



2.72.79 
3.29-89 

2«.II 2 

5-1549 
2-3-1291 
61-127 
22.13.149 

3 s '7-4i 



2.3877 

3-5-H-47 
22.7.277 

2-3 2 -43i 
24.5.97 

7. 1 109 

22.3.647 

5-^553 

2-H-353 

3 2 *86 3 

28.971 

17-457 
2-3-5-7-37 

19.409 
22.29.67 

3-2591 
2.132.23 

5 2 -3" 

2 5. 3 5 

7-ii-ioi 
2-3889 

3-2593 
22.5.389 

3 x -25i 
2.3.1297 
43.181 
28.7.139 

3 2 '5-i73 
2.17.229 

13-599 
22.3.11.59 

2.5. 19.41 

3*7 2 -53 
24.487 

2-3 2 '433 

5-1559 
22.1949 

3'23-"3 

2-7-557 
11.709 

2 3 -3-5 2 'i3 



148 



BROWN & SHARPE MFG. CO. 



From 
To 



7800 
7850 



7850 
7900 



7900 
7950 



7950 
8000 



8000 
8050 



8050 
8100 



o 

1 
2 
3 
4 

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9 
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12 
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16 

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18 

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33 
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45 
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54 
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87 
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27.61 

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73.107 

22.32.7.31 

13.601 

2.3907 

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2-5 a -i57 

3.2617 

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2.3.7.11.17 

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2.3929 

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22.7.281 
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2-3 2 -439 
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2.38.5.29 
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2 2 -3-653 

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2.3919 

32.13.67 

2 *. 5 . 7 2 



2.3.13.101 
28.5.197 

3-37-71 
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2.5.13.61 

7.11.103 
22.3.661 



2.3.1307 

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2 2 -37-53 

3-5-523 

2-3923 
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28.32.109 

47.167 

2-5 2 -i57 



2 2. 3 3. 73 

5-I9-83 
2-3943 
3. 1 1.239 
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78.23 

2-3-5-263 

13.607 
22.1973 
32.877 
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5-1579 
28.3.7.47 

53- H9 
2-1 1-359 
3-2633 

2 2 -5 2 -79 



2.3967 

3'5-23 2 
28.31 

2-3 4 -7 2 

17.467 

2 2 -5-397 
3-2647 

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2 8 -3-33 x 

5-7-227 

2-29-137 

3 2 -883 

22.1987 

2 '3-5 2 -53 



2 4 .7»7i 

3.11.241 

2.41.97 

5-37-43 
2 2 -3 a -i3-i7 

73-I09 
2.23.173 

3-7-379 
28.5.199 

19.419 
2-3-1327 

2 2 . 11. 181 

3 8 -5-59 
2.7.569 

3I-257 
2 5 -3'83 
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2-3 2 '443 

52.11.29 

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23-347 
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61*131 
2 3 -3 3 -37 



2.7.571 

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2 2 «i999 

11.727 

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26.58 

3 2 -7-i27 

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5.1601 
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2.52.7.23 

83-97 
22.3.11.61 

2.4027 

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7.1151 
2.3.17.79 



2.32.5.89 



22.2003 

3.2671 

2.4007 

5.7.229 

2 4 -3-i67 

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3 6 .ii 

22.5.401 

13.617 
2.3.7. 191 
71. 113 
28.17.59 
3.52. io7 
2.4013 

23-349 
22.32.223 

7-3J-37 
2.5.11.73 

3.2677 

2 5 -25l 
29.277 
2.3. 13. 103 
5-I607 
22.72.41 

3 2 -i9'47 
2.4019 



2 2 -5-i3-3M 

3-2687 

2.29.139 

"•733 

2 7. 3 2. 7 

5-l6l3 

2.37.IO9 

3-2689 

22.2017 

2.3.5.269 

7-"53 
28.1009 

3 8 - J 3-23 
2.11.367 

5 2. I7 . I9 
22.3.673 
41.197 

2-7-577 
3-2693 

2 4 .5«IOI 



2.32.449 
59-137 

2 2 -43'47 
3-5-7 2 -" 
2-13-311 



28.3.5.67 

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2.4021 

3-7-383 

22.2011 

5.1609 

2.38.149 

13.619 

2 4 -503 
3.2683 

2 '5 2 -7-23 



2 8 -3-337 
2.5.809 

32.29.31 
22.7.172 



2-3-19-71 
5-1619 

2 5 « II.23 
3.2699 
2.4O4Q 
7.I3.89 



BROWN ft SHARPE MFG. CO. 



I49 



Ffom 
To 



8100 
8150 



8150 
8200 



8200 
8250 



8250* 
8300 



8300 
8350 



8350 
8400 



o 

1 
2 
3 
4 
5 
6 



9 
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29 
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33 
34 
35 
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3 

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40 

41 
42 

43 
44 
45 
46 
47 
48 
49 



50 
51 
53 
53 
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55 
56 
57 
58 
59 
60 

61 
62 
63 
64 
65 
66 
67 
68 
69 
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72 

73 

74 
75 
76 
77 
78 
79 
80 

81 
82 

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87 
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2»-3 4 -5 a 

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2«5 2 -i63 
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2 3 .IOI9 

31.263 
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5-7-233 
2 2 -2039 

3-27I9 
2.4079 
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26.3.5.17 



24.3.132 

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2.4057 

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2.7.11.53 

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2.32.11.41 

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3.2707 
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2 2 -3-677 
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2.17.239 

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22.19.107 

3.2711 

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5.1627 

28.32. II3 

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3-27I3 

22.5.11.37 

7. 1 163 
2-3-23-59 
17-479 
24.509 

3 2 -5-i8i 
2-4°73 

22.3.7.97 

29.281 

2-5 2 -i6 3 



28.1021 
3-7-389 
2-5-19-43 



2 8 - 5 2 -4i 

59-139 

2.3.1367 

13.631 

2 a -7-293 

3-5-547 

2-H-373 

29.283 

24.38.19 

2.5.821 

3-7-I7-23 
22-2053 

43-i9i 
2.3.373 

5-31-53 
28.13.79 

3 2 ' 11-83 

2.7.587 



2-3.58. 11 

37-223 
2 2 .2063 

3 2 -7-i3i 
2.4127 

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2 6 -3'43 
23-359 
2.4129 

3*2753 
2 2 -5-7-59 

11.751 
2.35.17 

28.1033 
3-5-I9-29 
2-4133 
7.1181 

2 2 -3' I 3-53 



2 2 -3'5-*37 



2 2 -3 3 .227 

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2.61-67 

3-5 2 -io9 
2 4. 7 . 73 

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2.3.29.47 

2 2 -5-409 

34.101 

2.4091 

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28.3.11.31 

5^637 

2.4093 

3.2729 

2 2 .23-89 

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5.II.I49 

22.3.683 

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2.4111 

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2 3 -3-7 3 

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2.5.827 

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2-3- J 373 
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25.7.37 

3 3 -3Q7 
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22.32.229 

5-17-97 
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3-2749 
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2.11.13-29 

3-5-7-79 
28.17.61 

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3.2767 

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28.1039 
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22.2081 

3 2 '5 2 -37 
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3-2777 

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13.641 

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5.1667 

24.521 

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31.269 

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19-439 

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3 4 -io3 

28.7.149 

5-1669 

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17.491 

22.2087 

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2.52.167 



2.52.167 

7- 1 i93 
25.32.29 

2-4177 

3-5-557 
22-2089 
61.137 
2.3.7.199 

I3-643 
28.5.11.19 

32.929 

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5-7-239 
2.47.89 

3-2789 
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2-3 8 -5-3 I 

11.761 
22.7.13.23 

3-279I 

2-53*79 

58.67 

2 3 -3-349 

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3 2 '7 2 -i9 
22.5.419 

172.29 

2.3.11.127 

83.101 

2 6 »I3I 

3-5-13-43 
2-7-599 

22.32.233 

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2.17.277 

2 2 -3\5-i57 



22.3.11.71 
7. 13. 103 
2.43.109 

3-5* 
2 5.293 

2.32.521 

83.113 

22.5.7.67 

3-53-59 
2.4691 

"•853 
23.3.17.23 
5.1877 
2. 13.192 

3 2 -7-H9 
22.2347 
41.229 
2-3-5-3 I 3 



2.38.173 

2 7 -73 

3-5-7-89 

2.4673 

I3-7I9 
22-3.19.41 

2.52. 11. 17 



2*-587 
3.31. 101 
2-7.11.61 

5-1879 
22.34.29 

2.37.127 

3-13-241 

2 3 -5 2 -47 



2.7.673 

3 8 -349 
2 4 - 19.31 

5 2 -i3-29 
2-3-I57I 
11-857 

2 2 -2357 
3-7-449 
2.5.23.41 



2 8. 3 2. I3I 

2-53-89 

3-5-17-37 

2 2 -7-337 

2.3.112.13 

2 5 -5-59 

32.1049 

2.4721 
7.19.71 
22.3.787 
5.1889 

2-4723 
3.47.67 

2 3 .Il8l 

11.859 

2-3 3 -5 2 -7 



2.38.52.7 

I3-727 
22.17.139 

3-23-I37 
2-29.163 

5-3i-6i 
24.3.197 

7 2 -i93 
2.4729 

3 2 - io 5* 
22.5.11.43 



2 2 -5 3 -i9 

3-3i67 

2-4751 

13-17-43 
25.33.11 

5.1901 
2.72.97 

3-3169 
22.2377 

37-257 



2.3.19.83 

28.7.132 

3-5-63I 
2-4733 

22.32.2*63 

17-557 
2-5-947 

3.7.11.41 
2 8 -37 

2-3-1579 

5 2 -379 

22.23.103 

3 6 - x 3 

2.7.677 

2 3 -3'5-79 

19.499 

2.11.431 

3.29.109 

22.2371 

5.7.271 

2.32. 17.31 

53- J 79 
2 4 -593 
3-3i63 
2-5-13-73 



22.^.7.113 
11.863 
2.47. 101 
32.5.211 
2 8 -ii87 



28.29.41 

3 2 -7-i5i 
2-67.71 

5-H-I73 
22.3.13.61 

31-307 
2-4759 
3. 19. 167 

24.5.7.17 



2.32.232 

89- 107 

22.2381 

3-5 2 -"7 

2-H-433 

7-1361 

2 3 -3-397 

13-733 

2-5-953 

3 s -353 
22.2383 

2.3.7.227 

5-1907 
2M49 
3.11.172 
2. 19.251 

2 2 -3 2 '5-53 



29.47 

13-369 
31.81 
3.1193 
23-83 
3-37-43 



2.52. 191 

24.3.199 

4I-233 
2. 17.281 

3'5-7 2 -i3 
22.2389 

19-503 

2-3 4 '59 
112.79 

28.5.239 

3-3187 
2.7.683 

73-13! 
2 2 .3.797 

5-i9 I 3 

2-4783 

32.1063 

25.13.23 

7.1367 

2.3.5.11.29 



17-563 
22.2393 

3-3J9I 

2.4787 

5 a -383 
28.32.7. 

61-157 
2.4789 

3-3i- io 3 
2 2 .5.479 



19 



2-3-1583 

7-23-59 
22.53.19 



2.7.11.31 

2.1061 

■5 2 -i9i 



ii« 13-67 

2-3- J 597 

7-37 2 

2 4 -599 

3 3 -5-7i 

2-4793 

22.3.17.47 

43*223 

2-5-7' I 37 

3-23-I39 

2 3 » II-I09 

53-i8i 

2-3 2 ' I 3-4 I 

5.19.101 

22.2399 

3*7-457 

2-4799 

29-331 

2 7 -3-5 2 



154 



BROWN ft SHARPE MFG. CO. 



From 
To 



9600 
9650 



9650 
9700 



9700 
9750 



9750 
9800 



9800 
9850 



9850 
9900 



o 

I 
2 
3 
4 
5 
6 

7 
8 

9 
10 

11 
12 
13 
14 

3 

19 
20 

21 
22 
33 
24 
«5 
26 

27 
28 

29 
30 

31 
32 
33 
34 

36 
37 
38 
39 
40 

41 
42 
43 
44 
45 
46 

47 
48 
49 
[30. 



50 
51 
53 
53 
54 

it 

9 

60 

61 
62 
63 
64 

II 
is 

69 
70 

71 
72 

73 
74 

76 
77 
78 
79 
80 

81 
82 
83 
84 
85 
86 

87 
88 

89 
90 

9i 
92 
93 
94 

96 
97 
98 
99 
100 



2 7 -3'5 3 



2*4801 
32.jx.97 

22.74 

5-i7-"3 
2.3.1601 

13-739 

2 3 -I20I 

3-3 2 °3 
2-5-3I 2 

7-1373 
22.33.89 

2. 11. 19.23 

3-5-64I 
2 4 -6oi 

59-163 
2.3.7.229 

32.1069 
2.17.283 

23.3.401 

5 3 -7-n 
2.4813 

3-3 2 o9 
22.29.83 



2.32.5.107 



2S.7.43 

2.4817 

5-4J-47 
22.3.11.73 

23-419 
2.61.79 
34.7.17 
23.5.241 

31-3" 
2.3.1607 

22.2411 

3-5-643 

2-7-13-53 

11.877 

24.32.67 

2-5 2 -i93 



2-5 a 'i93 

3-32I7 

22.19.127 

7 2. 197 
2.3.1609 

5-J93 1 
23.17.71 

3 2 -29-37 
2-H-439 
13-743 
^ 2 -3'5-7-23 



2.4831 
3-3221 

2 6 -I5I 

5-1933 
2.33.179 

7.1381 

22.2417 

3- "-293 
2.5.967 

I9-509 
23.3.13.31 

17-569 
2.7.691 

3 2 '5 2 -43 
22.41.59 

2-3-1613 
24.5.112 



3.7.461 
2.47.103 
23.421 
22.32.269 

5-I3-H9 
2.29-167 

3-3229 
23.7.173 



32.52.97 

89.IO9 
2-32.72.!] 

3i-3 J 3 
23.1213 

3-5-647 
2.23.211 

I7-57I 
22.3.809 
7.19.73 
2.5.971 

3 2 -i3'83 

24.607 

11.883 

2-3-1619 

5.29.67 

22.7.347 

3-4 J -79 
2-43-113 



2-3-5 8 -i3 
72.199 

2 s -23-53 

3-325I 
2.4877 

5' 1 95i 
22.32.271 

11.887 

2.7.17.41 

3-3253 
2 5 -5.6i 



43-227 
2.3.1627 

I3-75I 
22.2441 

3 2 -5-7-3i 
2.19.257 



23.52.72 

2.132.29 

2 2 -3-!9-43 

5-37-53 

2-4903 

3.7.467 

24.613 

17-577 
2.33.5.109 



22.11.223 

3-327I 
2.7.701 

5-i3-i5i 
23.3.409 



23.35.5 



2.4861 
3-7-463 

2 2 . II. 13.17 

5 2 -389 

2.3.I62I 
71-^7 

2».I9 

3 2 ' 2 3-47 
2-5-7-139 

37-263 
22.3.811 

2-3" I 57 

3-5-"-59 
28.1217 

7. 13. 107 
2-3 2 '54 I 



2.3.5.17.19 

11.881 
22.2423 
3 3 -359 
2-37-I3I 

5-7-277 

2 4 «3.IOI 



2-13-373 
3-53-61 

2 2 -5 2 '97 



22.5.487 

3.17.191 

2.4871 

24.3.7.29 
5-1949 

2-H-443 
33.192 

22.2437 
2-3'5 3 -i3 



2 3 -3-n-37 

2-5-977 

3-3257 
2 2 .7.349 

29-337 

2.33. 181 

5 2 -i7-23 
2^13.47 

3-3259 
2.4889 
7. 11. 127 
2 2 -3-5-i63 



2.67.73 
32.1087 
28.1223 
5. 19. 103 
2-3-7-233 

22.1247 

3-13-251 
2.5.11.89 



26.32.17 
7-1399 

2-59-83 

3-5-653 
22.31.79 

97.101 
2.3.23.71 

4 x - 2 39 

28.52.72 



2.4909 

32.1091 

22.5.491 

7.23.61 
2.3.1637 
1 1. 19.47 
28.307 

3-5 2 -i3! 

2.173 

3I-3I7 
2 2 -3 3 -7-i3 

2-5-983 

3-29-113 
23.1229 



2.52.197 

2 2. '3.82 1 ' 
59.167 
2-13-379 
3 3 -5-73 

2 7 «7.II 

2-3-31-53 
22.5.17.29 

3- J 9-i73 

2-4931 

7.1409 

2 8 -3 a -i37 

5-1973 

2-4933 

3.11. 13.23 

22.2467 

7i-i39 

2-3-5-7-47 



2 4 «6i7 
32.1097 

2-4937 
5 3 -79 
22.3.823 
7.17.83 
2.1 1.449 

3-37-89 
28.5.13.19 

41.241 
2.34.61 



2.3.1 1. 149 

5.7.281 

22.2459 

3 2 -i°93 
2.4919 

2 4 -3-5-4i 

13-757 
2.7.19.37 

3-i7-i93 

22.23.107 

5.11.179 

2-3 2 -547 

43.229 

28.1231 

3.72.67 

2.52.197 



2 a -7-353 

3-5-659 

2-4943 

25.3.103 
11.29.31 
2-5-23-43 

3 2 -7-i57 
22.2473 
13.761 
2.3.17.97 

5-1979 
28.1237 

3-3299 
2.72. 101 

19-521 
2 2 «3 2 *5 2 *iil 



BROWN & SHARPE MFG. CO. 



'55 



From 
To 



9900 
9950 



9950 
zoooo 



IOOOO 

Z0050 



10050 

IOIOO 



IOIOO 

10150 



10150 
10200 



9 
zo 

zz 

12 

13 
14 
15 
16 

17 

18 

19 
20 

2Z 
22 
33 
34 
«5 
26 

37 
28 

39 
30 

31 
3« 
33 
34 

» 

3 

39 
40 

41 
43 
43 
44 
45 
46 

48 
49 
5Q 



50 
51 
53 
53 
54 

56 



60 

61 
62 
63 
64 
65 
66 
67 
68 

69 
70 

7i 
73 
73 
74 

76 

77 
78 

II 

81 
82 
83 
84 
85 
86 

87 
88 

89 
90 

91 
93 
93 
94 

96 
97 
98 
99 
zoo 



2 2 -3 3 -5 2 -" 

2-4951 
3-33°i 
2 4 -6io, 

5.7.283 
2.3.13.127 

22.2477 

3 8 -367 
2.5.991 

"•17-53 

2 3 -3'7-59 

2 3-43i 

2-4957 

3-5-661 

22.37.67 

47.211 

2.32.19.29 

7.13. 109 

2 6 -5-3i 

3-3307 

2.II 2 «4I 



2.52.199 
3.31. 107 

2*.3II 

37.269 
2.32.7.79 

5.11.181 
22.19.131 

3-3319 
2-13-383 

2 3-433 
25.3.5.83 

7-H 2 3 

2-17-293 

3 5 *4i 

2 2 -47-53 

5-1993 

2.3.11.151 

24.7.89 
3-3323 
2-5-997 

i3 2 -59 
22.32.277 



22.3.827 

5 2 '397 
2.7.709 
32.H03 
28.17.73 

2-3-5-331 



22,13.191 

3-7- "-43 
2.4967 
5.1987 
24.33.23 

x 9-5 2 3 
2.4969 

3-33I3 
22.5.7.71 



2.3.1657 
61-163 

2 3 .II.II3 

2-4973 
78.29 

22.3-829 
2-5 2 -i99 



2.4987 

3-5 2 -7'i9 
28.29.43 

11.907 
2.3.1663 
17.587 
22.5.499 

32.1109 
2.7.23.31 
67.149 
28.3.13 

5-1997 

2-4993 

3-3329 

22.11-227 

7.1427 

2-3 3 -5-37 

97.103 
28.1249 

3-3331 
2.19.263 

5-1999 
22.3.72 17 

I3-769 
2-4999 
3 2 .ii«ioi 

2*vS* 



2 4 -5* 

73- J 37 

2-3-1667 

7.1429 

2".4i.6i 

3-5-23-29 

2-5«>3 

2 8 «3 2 -i39 

2.5.7.11.13 

3-47-71 

22.2503 

x7.19.31 

2.3.1669 

5-2003 

28.313 

3 8 -7-53 
2.5009 

43-233 „ 
22.3.5.167 

11.911 
2.501 1 

3' I 3-257 
28.7.179 

52.401 
2-3 2 '557 
37-271 
22.23-109 

3-3343 
2-5- J 7-59 

7- H33 
2 4 .3«n.i9 
79.127 
2.29-173 

3 2 '5-223 
22.13.193 

2-3-7-239 
28.5.251 

3-3347 
2.5021 
112.83 
22.34.31 

5-7 2 -4i 

2- 5023 
3. 1 7- 197 

2 ft -i57 
13-773 
2-3-5 2 -67 



2.3.52.67 
19.232 

2 2 -7'359 
32.1117 

2.11.457 

5.201 1 

28.3.419 

89.113 

2.47.107 

3-7-479 

2 2 -5-503 



22.52.101 

3-7-13-37 
2-5051 

28.3.421 

5-43-47 

2.31. 163 

32.1123 

22.7.192 

11.919 

2-3-5-337 



2-3 2 ' I 3-43 

29-347 
24.17.37 

3.5.11.61 

2.7.719 

22.3.839 
2-5-19-53 

3 s -373 
28.1259 

7-H39 
2-3-23-73 
5 2 -i3'3i 
22.11.229 

3-3359 
2.5039 

28.32.5.7 

17-593 
2.71 s 

3-336i 

22.2521 

5.2017 

2.3.412 

7.11.131 

28.13.97 

3 a '*9-59 
2.5.1009 



2 7 -79 

3-3371 

2.13.389 

5-7-I7 2 
22.32.281 

67-151 

2-5059 

3-3373 
28.5.11.23 

29-349 
2.3.7.241 

53-i9i 
22.2531 

2.61-83 

13.19.41 

24.3.211 

7-1447 
2.5-1013 

3- "-307 
22.17.149 



2-3 8 -563 

5.2027 

28.7.181 

3-3 I ' I °9 

2-37-137 

2 2 -3-5-i3 2 



22.3.292 

2.72.103 

3-5-673 
24.631 

23-439 
2.38.11.17 

2 2 .5 2 »IOI 



2.11.461 

3 2 -7 2 -23 
28.317 

5.2029 
2.3.19.89 
'/3-I39 
2 2 -43-59 
3.17.199 

2-5 2 -7-29 



2.52.7.29 

2»-3 8 '47 
11. 13.71 

2-5077 
3-5-677 
22.2539 

7. 145 1 
2.3.1693 

24.5.127 

32.1129 
2*5081 

22.3.7.112 
5. 19. 107 
2. 13. 17.23 

3-3389 
28.31.41 

2-3 2 -5-"3 

7-1453 

2 2 -2543 

3-3391 

2.5087 

52.11.37 

2 8 -3-53 

2.7.727 
38.13.29 

2 2 -5-509 



2.3.1697 

17-599 
28.19.67 

3-5-7-97 
2. 11.463 
61.167 
22,32.283 

23-443 
2.5.1019 

3*43-79 
2 4. 7 2.i 3 

2.3.1699 

5-2039 

22.2549 

32.11.103 

2.5099 

7-31-47 

a s -.*5 a -'7l 



Decimal Equivalents 



i5» 



BKOWN * SHARPE MFG. CO. 



DECIMAL EQUIVALENTS OF PARTS OF AN INCH. 



A 



z-x6 



A 



1-8 



A 

A 

J - 



3-16 



if 



A 



H 



1.4 



H 



A 



if 



5-16 



.01563 
.03125 
.04688 
.0625 

.07813 
.09375 
.10938 
.125 

.14063 
.15625 
.17188 
.1875 

.20313 
.21875 
.23438 
.25 

.26563 
.28125 
.29688 
.3125 




|f ... .70313 

If 71375 

H ... .73438 
3-4 75 

If ... .76563 

M 78125 

fi ... .79688 
13-16 8125 

f| ... 82813 

H 84375 

|f ... 85938 
7-8 875 

ff ... .89063 

•H 9062 5 

ff ... .92188 
15-16 9375 

ft ... .95313 

»' 96875 

ff ... .98438 
1 1.00000 



BROWN & SHARPE MFG. CO. 



159 



TABLE OF DECIMAL EQUIVALENTS OF MILLIMETRES AND 
FRACTIONS OF MILLIMETRES. 



mm. Inches. 


mm. Inches. 


mm. Inches. 


mm. Inches. 


m ^=.00039 


ft — .01399 


ft — .03530 


ft - -03740 


ilo — -00079 


% = .01339 


ft — .03559 


ft — .03780 


ft — .00118 


ft - - 01378 


ft- .03598 


ft = .03819 


1J0 = .00157 


ft — -° 141 7 


ft -.02638 


ft — .03858 


ft — - 00197 


ft - -01457 


ft- .02677 


"?00 "^ — .IKJotfo 


ft = .00236 


ft — .01496 


ft - .02717 


1 — .03937 


^ = .00276 


ft- -01535 


ft «.02756 


3 = .07874 


ft = .00315 


ft = .01575 


ft -.03795 


3 — .11811 


ft = .00354 


ft — -oifti* 


ft = .03835 


4 = .15748 


^=.00394 


& - -01654 


ft -.02874 


5 = .19685 


ft — .00433 


ft - -01693 


ft - .02913 


6 — .23622 


ft — -00*72 


ft = .01732 


ft = .02953 


■7 — J37559 


ft = .00513 


£ — -01773 


ft = .02992 


8 = .31496 


ft—. 00551 


& - .01811 


ft = . 03032 


9 = .35433 


ft — -005W 


ft — .01850 


ft = .03071 


10 — .89370 


ft = .00630 


ft — -01800 


ft — .03110 


11 » .43807 


ft - .00009 


ft - .° 19S9 


ft- .03150 


13 — .47344 • 


ft == .00709 


ft — .01969 


ft — .03189 


13 — .51181 


ft = .00748 


ft — -02008 


ft =.03228 


14 — .55118 


ft = .00787 


ft — -03047 


ft = .03368 


15 — .59055 


ft = .00827 


ft — . 02087 


ft =.03307 


16 = .63993 


100 == -00806 


ft =.03136 


ft = .03346 


17 = .66939 


ft = .00006 


ft— .02165 


ft = .03386 


18 — .70866 


ft — .00945 


ft =.02205 


ft = .03435 


19 = .74803 


ft — . 00984 


ft- .02244 


ft — . 03465 


30 — .78740 


ft — -01024 


ft« .02283 


ft -.03504 


21 = .83677 


ft — .01063 


ft- .02323 


ft -.03543 


28 = .86614 


£ - .01102 


ft — . 02363 


ft — .03588 


33 — .90551 


ft — .01143 


ft- .02*02 


ft -.03633 


34 = .94488 


% - .01181 


ft -.02441 


ft -.03661 


35 = .98435 


ft = .01330 


ft- .02480 


ft — .03701 


36 =1.03363 


ft — -01360 















V? 



;..'■ % »r 









'V* ,-. *.: 



■-* 'A ;:'v < 









* • » ' * </ 



-A 









,'OAv 






.^v 






* * -k ; 



•^;V ' s ,1 












/•■'■ -•;;,* >^-> ■;►*:-. ^ 






•* -*' 



> 




" V 






V 



■•.■fv.r. 



i 



*>A ' 



K '■" 






y;-. v. 



r (■'• 






I ' / if . -' * * i •• a i . • 










ftfcst^ 



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